In Greek mythology, Agathon is one of the sons of King Priam of Troy by women other than Hecuba. Homer names him among the nine sons Priam chides when preparing Hector's ransom; Apollodorus and Hyginus count him among Priam's children, and Dictys has him slain with brothers by Ajax son of Telamon.
Adapted from Wikipedia, "Agathon (mythology)" · CC BY-SA 4.0
I.Son of Priam
Handbook tradition places Agathon among Priam's sons by concubines rather than by Hecuba. In Iliad 24 Priam summons nine sons — Helenus, Paris, Agathon, Pammon, Antiphonus, Polites, Deiphobus, Hippothous, and Dius — and wishes they had fallen in Hector's place.
Apollodorus lists him among the king's children; Hyginus likewise. Dictys Cretensis reports that Agathon and his brothers Antiphus, Agavus, and Glaucus were all slain by Ajax son of Telamon — a late prose variant beside the Homeric roll-call.
II.Homonym care
The atlas id agathon-trojan is the Priamid alone. Not the Athenian tragic poet Agathon, nor any later historical bearer of the name.