I found this coin with the head of Kabeiros wearing a conical pilos (pileus) to be of interest, as he was a protector of sailors. The pilos was a brimless, felt cap worn by sailors in ancient Greece, and later copied by ancient Rome. The cap became emblematic of liberty and freedom from bondage. During the classic revival of the 18th and 19th centuries it was widely confused with the Phrygian cap, which appeared frequently on statuary and heraldic devices as a "liberty cap."
The coin is full of mystery, from the history of Birytis, to the cult of the Cabeiri. In Greek mythology, the Cabeiri, were a group of enigmatic chthonic deities. They were worshipped in a mystery cult closely associated with that of Hephaestus. The Cabeiri were given a mythic genealogy as sons of Hephaestus.

I could find very little information about Birytis apart from the text below, and the site is tentatively located near Mersinoba, Asiatic Turkey.
From "The Hellenistic Settlements in Europe, the Islands, and Asia Minor" By Getzel M. Cohen:
The discovery and identification of the Cal Dag as the site of Kebren was made by F. Calvert, who published his findings in Arch. Journal 22 (1865). According to Calvert, of seventy-one coins found at the site and immediate vicinity, twenty-five were of Kebren.
Imhoof-Blumer suggested that Kebren was renamed Antioch, and noting the appearance of the letters B and K on the reverse of some coins, Robert hypothesized that they referred to Birytis and Kebren. The conclusion being that Kebren and Birytis were united in a sympoliteia or synoecism, and together were included in the new Antioch.
Cook noted that Strabo explicitly only mentions Kebren and Skepsis in the original synecism of Antigonei, but suggested that some of Strabo's discussions implied that other towns were also included in Antigoneia. Since Strabo explictely lists Skepsis as one of the towns involved, and since it was still independent in 311/0 BC, Antigoneia could not have been founded before that date. Although there is no supporting evidence, Robert suggests that Birytis was also included in the synoecism. Cook on the basis of the evidence of bronze coins of Birytis, which were probably minted after the end of the fourth century, ie., after the synoecism, rejected this view.
As for the location of Antioch, Cook surmised it was a settlement of exiles at a distance from their old home. He noted the absence of Antioch coins from the Cal Dag and in fact from the Troad. Cook suggested that a dedication of Roman date from the vicinity of Kyzikos to Dionysos Kebrenios might "offer a clue" to the location of Antioch. I. Robert, BCH 106 (1892) suggested that Antioch may have been centred at Birytis rather than at Kebren, however the location of Birytis is not secure. I. Robert has argued it was close to Kebren, but Cook would look for it "in the northwest Troad in the close vicinity of Ilion." (Ilion being the Archaic name for the pre-classical city of Troy, hence the title of Homer's Iliad.)
From "An Inventory Of Archaic And Classical Poleis." Edited by Mogens Herman Hansen and Thomas Heine Nielsen.:
Birytis is shown on Map 56 of the Barrington Atlas, but this location, at Mersinoba (Cook 1973), is not beyond doubt. The city is recorded in the Athenian tribute lists, but late 4th century coins have the form ΒΙΡΥ. No Archaic or Classical source calls Berytis a polis, and the retrospective mentions in Steph. Byz. do not indicate a source. However, the community issued its own coinage in the late 4th century BC. The external collective city-ethnic is recorded in the Athenian tribute lists, and the internal by coins of the 4th and 3rd centuries BC.
Birytis was a member of the Delian League. It presumably belonged to the Hellespontine district, and is recorded from 454/3 to 446/5 BC a total of six times, once completely restored, paying a phoros of 1,000dr. It was assessed for tribute in 425/4 BC. However, it is not completely certain that the Berysioi are to be identified as the inhabitants of the polis mentioned by Steph. Byz.
Birytis struck coins of silver and bronze in the late 4th century to the early 3rd century. Silver:obv. head of Herakles; rev. head of beardless Kabeiros wearing pilos between two stars. Bronze:obv. head of beardless Kabeiros wearing pilos; rev. club, or triskeles; legend: ΒΙΡΥ; L. Robert (1951) 25-31, SNG Cop. Troas 247-53).
Wildwinds only shows seven varieties of bronze coins, and one of silver.

Troas - Birytis. c. 300 BC.
Obverse: Head of Kabeiros left, wearing pileus. Reverse: Club, B-I / P-Y, all enclosed in wreath. Bronze. Diameter: 11 mm. Weight: 1.2 gr.
Reference: BMC 7-8; SNG Copenhagen 250