To start, we should say that 'modern' Buscemi is a town of Arab origin - but although this is a historical truth it is also a glaring over-simplification.
In fact, the site of Buscemi has a very ancient history, which over the centuries has attracted much interest among scholars, and disputes about its origins which continue to this day...for your interest we include rather lengthy details and discussions:
Origins of Buscemi
To realize the importance of the archaeological site of Buscemi, there's nothing better than starting with the words of Paolo Orsi (1859-1935), whose discoveries established a long and fruitful period of researches.
19th century adventures of Paolo Orsi in Buscemi
Although quite lengthy the following passages are also interesting and bear repeating:
"[...] Buscemi is a large village in the Syracusan high mountains (alt. 750m) in the upper reaches of the river Anapo; it is in front of Palazzolo, the ancient ‘Akrai’, divided from it by a broad and deep valley, at the bottom of which the river flows. The oldest data referring to Buscemi dates back to the 12th century, but the name of Buscemi is of Arabic origin, and the village is mentioned several times in the “Italia descritta nel Libro del Re Ruggero” .
However, the archaeological explorations can be traced back well over several centuries. Attracted by discoveries on the site, I spent almost all of November 1897 circling it in each direction, so that I can say that I know it very well. The local oral tradition, which I consider correct, says that Buscemi before the 18th century did not arise on the current site, but on the opposite small hill called St. Nicholas, flattened on top, with steep descents, open and sunny and somewhat protected from northerly winds, hence suited for an ancient village.
In the craggy rocks of the western and southern slopes I found fifty sepulchral chambers of the third Sicilian period (fifth-seventh centuries BC), which, being in a totally naked land, were 'ab antiquo' robbed of everything, and indeed many of them were turned into small Christian underground vaults, dating back to the fifth-seventh centuries BC. On top of this small hill I then found some Greek graves, all explored by peasants.
A couple of kilometers north of the village, the mountain is crossed by the ‘Cava S. Georgio’, in whose top there is a Sikan necropolis with about sixty other small rooms, and specifically in the site called ‘Geràme’. I explored one third of them, finding all the others are empty, and according to the few bronzes and pottery collection, I decided that the necropolis dates back to the end of the second Sicilian period ('Notizie degli Scavi', 1898, p. 37) [...]” .
In addition P. Orsi discovered several inscriptions, although many of them were mutilated and very difficult to interpret. However, about some of them the eminent archaeologist gave an excellent essay of his expertise, providing guidance that was later developed, bringing more knowledge about the origin of ancient peoples who inhabited the site of Buscemi, which could be the mythical "Herbessos", of which Ptolemy (100-175 AD) had spoken:
"[...] If the numerous inscriptions that lined the walls of the large rooms, and especially the second, had been seen by us in good condition, in such a way as to allow a thorough reading of them, the origins of the caves and their cult would be promptly clarified. Instead, with their “tituli” (inscriptions) mutilated, I have reached only a partial interpretation of them (...) A lot of them have lists of names preceded by a chronological indication; the most complete inscription (No. 3) lists the names of Roman consuls of 35 AD, and that of the 'Amphipolos ton paidon" of the city, to whom the sanctuary and "iereia" were referred.
The "anphipolos" was a priestly dignity of which we have only two samples in Sicily, at Syracuse (Kaibel 9) and Centuripe (K. 574). From Diodorus [90-27 BC] (XVI, 70) we know that in Syracuse there was still the “anfipolos Dios Olimpios” (...) But what were the gods to the cult of which the priests devoted themselves?
The inscriptions repeatedly remind us of (...) two deities, probably feminine and virgin sisters, but who the "Theai paides" were, now for the first time revealed by the inscriptions of Buscemi, is not easy to determine, missing all records of them in texts, inscriptions and coins.
However, we can suggest an allusion to the Muses (also supported by the presence of Apollo), or ‘Charites’, but because the fundamental concept of the name indicates a feminine dualism, we think of Demeter and Cora, always jointly quoted because almost never separated, and revered at Tauromenio and Akrai as "agnai theai" (K. 204, 431), that is, as very holy goddesses.
Demeter and Cora are two Sicilian goddess par excellence, which had a cult not only in all Greek cities but also in many Sikan cities (...) They are the goddesses who preside over the fertility of the land, the increasing number of herds; besides this they are the goddess of the mountains, water and forests, and preferably they have their religion and live in caves (...) These Nymphs had a special devotion not only to Syracuse (Atheneus VI, 250 A) but in the nearby Akrai (Kaibel 219) (...)
Less obscure is the deity called ‘Anassa’ (inscription 2), on a cult of which in Sicily there was no literary or epigraphic memory, but no one will hesitate to recognize in them the goddess Artemis, identified with the " Artemis Persiché" or " Artemis Anaitis", the goddess of fertility and vitality of nature [...]".
P. Orsi's long survey on the "Paides" also brought very interesting results from the ethnic point of view, as discovered by Margaret Guarducci who found that the people who inhabited this area were the ancient Sicules (in Latin ‘Siculi’, Greek “Sikeloi’).
The cult of "Anassa" referred to by P. Orsi was in fact an ancient Siculian and Roman cult; the Romans kept a special devotion to the goddess "Anna", the goddess of fertility. It was highlighted by Margaret Guarducci in an essay of 1934, in which she wrote:
"What may particularly attract our attention are the same deities worshipped in the sanctuary of Buscemi (...) The cult of "Anassa"-Anna leads to a conclusion on which historians and linguists agree, that is the Latins and the Sicules belong to the same ethnic layer, the first wave of Indo-European peoples who had invaded the whole Italian peninsula, also passing the Strait of Sicily (...) The presence of "Anna" among the Romans and the Sicules would confirm the original unity of these two peoples" 
The conclusion of M. Guarducci has been confirmed by contemporary studies:
"Around a triad of paides, Graecised in Kore, Artemis and Athena, Anna is venerated in a Shrine Cave and has the benevolent characteristics of a pre-Greek mother. In the name lives the Akkadian 'anna', 'annu' (consent, approval, positive divine answer to a query)" 
With regard to the relations with the cult of "Anna Peranna" among the Romans, it suggested "the beginning and the end of the year. This concept was affirmed more and more, and the goddess (…) was finally invoked as the goddess of the year, attested by Macrobius (5th century) with the verb ' annare ', or 'perannare '" .
Finally, P. Orsi also mentioned another thorny subject on the ancient Buscemi, denying that it could be identified with the ancient "Herbessos" (Latin "Herbessus"):
"[...] Finally, There is a topographical question (...) I have not found in Buscemi and its immediate boundaries archeological documents that prove the existence in the site of a Greek or Greek-Roman small town ... I know that some scholars, however with lack of evidence, would place the ancient Herbessus in Buscemi, but I think that this identification has not a leg to stand on. If so, there can be no doubt about the choice, the only nearby and important city which can boast of connections with our sanctuary is Akrai [...]".
So, while Ettore Pais claimed with great conviction that "Herbessus" was Buscemi, or was very close to it, P. Orsi was very skeptical. We also observe that the arguments of Ettore Pais were very convincing:
"[...] Herbessus held the food supplies of the Romans, when they besieged Agrigentum during the first Punic War. It was occupied with the betrayal by the Carthaginian General Hanno. Presumably then, the city was punished by the Carthaginians, as Diodorus said that it was devoid of inhabitants.
During the Second Punic War, 540 = year 214 (…) it is true that the city capitulated, submitting to the consul Marcellus, but it did not obtain the forgiveness of the Romans, since it became a ‘censoria’ city (...) Bearing this in mind I was eager to find the place where the ancient Herbessus stood, and I passed through the plateau overlooking Syracuse (...) Mr. Giovanni di Natale discovered an ancient necropolis here, around 1870.
I do not hesitate to place the ancient Herbessus here, where Hippocrates and Epidius retreated, after the capture of Leontini. The position of Buscemi also topographically corresponds to the Herbessus of Ptolemy, who placed the city near Leontini and Netum. It was one of the extreme western limits of the reign of Hieron [...]" .
The controversy between the supporters of these two opposing theories dragged on for the entire 20th century, with very uncertain results. Today, it "would seem" that Buscemi has lost ground in the debate, because "Herbessos" might now be identified with the “Montagna di Marzo, close to Agrigento, but the matter is far from settled with certainty.
The Byzantine era at Buscemi
The Byzantine period was very important for Buscemi, with some religious buildings of great historical and artistic prestige being built. Once again the discoveries of Paolo Orsi were fundamental:
"On the opposite side of the ravine there are two small Christian catacombs, (…) [and] a very ancient church, all carved in the rock and surrounded by graves and pit arcosolium: it was the ancient shrine of St. Peter" .
These ruins consist mainly of churches and rock sanctuaries, often attached to some monasteries. More recently we have a brief but exhaustive study of it:
"[...] At close range from Buscemi is located (…) a Sikan necropolis, consisting of tombs carved into the limestone. It was very easy, therefore, to use these spaces and turn them into churches; the walls were often painted with sacred images of which still remains some traces. In fact, the Sikan tombs were located in niches along the walls of the rooms, and these recesses were re-used by the Christians […]” .
Arab period, the Normans and Buscemi development
If the Byzantine period was important, the Arab times were crucial. In fact, "Buscemi" even derives from an Arabic name (see etymology below). During Norman times Count Roger's (1031-1101) son Geoffrey was invested with the county of Buscemi and under the reign of Frederick II of Swabia (1094-1250) it was ruled by Matthew Calvello:
“Frederick, Emperor of the Romans, grants and confirms to Matthew Calvello, his faithful, the city of Buscemi: Having determined the accuracy with which Matthew Calvello has served the Crown, we grant and confirm to him and his heirs in perpetuity the city of Buscemi" 
About Matthew Calvello, Huillard-Bréholles reminded us that he had also been invested with another feud by Rainald of Spoleto: “We, Rinaldo, by the will of God and Emperor Duke of Spoleto, grant to Matthew Calvello and his heirs in perpetuity the feud sited in ‘Goracio’ and its appurtenances" .
Buscemi from the 16th century
Matthew Calvello ruled Buscemi until the Wars of the Vespers, when the barony passed to the Ventimiglia family. In 1556 the county of Buscemi was granted to Giuseppe Requesens by a decree of King Philip II, and then the town remained under the rule of the Requesens, who were also the lords of Pantelleria.
Buscemi was located on Mount St. Nicholas, at an altitude of 759 metres, until 1693, but it was destroyed by a devastating earthquake. It was then rebuilt further down the hill, in a place adjacent to the old site. Although no documents have emerged showing the design, the reconstruction of the new town was marked by the Baroque style, as evidenced by the civil and religious buildings.
Buscemi today, thanks to its territory which is rich in archaeological remains, is open to international tourism.
Etymology and the origins of the name Buscemi
With regard to the etymology, F. Maurici stressed that surely Buscemi derives from a "nickname of an Arab man on the model of 'qal' at Abu Shammah ' - Buscemi therefore means ‘the fortress belonging to the man with the mole’” . This etymology is essentially shared by all specialists: "According to [others] Buscemi derives from the prefix 'Abu Samah', that is the '[man] full of moles'” .
What we do not know for sure is whether the term 'Qal'at' refers to the presence of a 'fortress' or to the nature of the place; in practice, we do not know if there was a fortress in Arab times; in fact:
"About these towers that dominated the valley of the river Anapo we know nothing. It is certain that Idrisi, citing the castle of Buscemi, use the technicism 'Qal'at' to mention the 'fortellicium' [small fortress] of Abu Samah. The technical term [Qal'at], as is known in Arabic sources, indicates a place fortified by nature and not necessarily a 'castrum' [Castle]" .
Before the advent of the Arabs, we do not know what was the name of Buscemi, maybe ‘Essina’" . G. di Marzo specified that "Buscemi is mentioned in a diploma of Alexander III (1100-1181), which describes the boundaries of the Diocese of Syracuse in 1108, and perhaps in another of Urban II [1040-1099] in 1093 under the corrupt name ‘Essina’ (...) or ‘Abisama’" 
See also the Buscemi travel guide.
1. Amari and Schiaparelli's edition, p. 53-55
2. See P. Orsi, “Buscemi. Sacri spechi con iscrizioni greche scoperti presso Akrai”, in “Notizie degli scavi di antichità comunicate alla R. Accademia dei Lincei”, Roma, 1899, pp. 452 sgg.
3. "Italy described in the Book of King Roger" by Idrisi [1099-1166]
4. See M. Guarducci, “Il culto di Anna e delle Paides nelle iscrizioni sicule di Buscemi, e il culto di Anna Perenna”, in “Studi e materiali di storia delle religioni”, 1934, pp. 30, 48-49
5. See G. Semeraro, “Le origini della cultura europea”, Olschki, 1984, Vol II, p. 173
6. See, “La parola del Passato”, 1972, p. 404
7. See E. Pais, “Alcune osservazioni sulla storia e sulla amministrazione della Sicilia ...”, 1888, pp. 153-156
8. See M.I. Gulletta, “Timoleonte, Entella e la sua 'Chora'”, in “Quarte giornate internazionali di studi sull'area elima” , 2003, II, p. 811 note 112
9. P. Orsi (“Nuove Chiese Bizantine nel territorio di Siracusa”, in “Byzantinische Zeitschrift”, 1899, pp. 613-642
10. See M. Laudani, “Breve ricognizione di alcune chiesette bizantine nella Sicilia orientale. Secoli VI-VIII” in “Porphyra”, 2006, VIII, pp. 77 - 79
11. See “Friderici Secundi Historia diplomatica”, collegit ... recensuit … disposuit et notis illustravit Jean-Louis Alphonse Huillard Bréholles , Parisiis, 1852, Vol III, pp. 156-157
12. As ref. 11, p. 157 note 1
13. See F. Maurici, "Castelli medievali in Sicilia ...", Sellerio, 1992, p. 70
14. G. B. Pellegrini (1972, p. 382), G. Caracausi (1983, p. 115 note 186) and G. Rohlfs (1984)
15. See S.C. Sgroi, “Interferenze fonologiche, morfo-sintattiche e lessicali fra l'arabo e il siciliano”, Centro di studi filologici e linguistici siciliani” , 1986, p. 134
16. See “III Congresso nazionale di archeologia medievale: Castello di Salerno, Complesso di Santa Sofia”, Salerno, 2-5 October 2003, All'insegna del giglio, 2003, Vol I, p. 496
17. See I. Peri, “Uomini, città e campagne in Sicilia dall'XI al XIII secolo”, 1978, p. 48
18. See G. di Marzo, “Dizionario topografico della Sicilia”, 1855, Vol I, p. 170