Amycus (Amykos) was king of the Bebryces in Bithynia, son of Poseidon and the Bithynian nymph Melia. He forced strangers to box him to the death; when the Argonauts landed, Polydeuces accepted the challenge and killed him, after which the Argonauts routed the avenging Bebryces. He is distinct from the centaur Amycus.
Adapted from Wikipedia, "Amycus" · CC BY-SA 4.0
I.King of the Bebryces
Amycus rules the mythical Bebryces on the Asian shore of the Bosporus. Mythographers make him son of Poseidon and Melia, a local nymph — a genealogy that marks his savage strength as a gift of the sea-god.
His custom is to compel arriving strangers to a boxing match and to kill them in the ring, a violation of guest-right that sets up the Argonauts' arrival as both ordeal and justice.
II.Bout with Polydeuces
When the Argo puts in to his land, Amycus challenges the crew's best fighter. Polydeuces (Pollux), the Dioscurus famed for boxing, takes the match. Apollonius Rhodius gives the fullest poetic bout; Apollodorus, Hyginus, and the Orphic Argonautica agree that Polydeuces strikes him dead — often with a blow that shatters elbow or temple.
The Bebryces rush to avenge their king; the Argonaut chiefs arm and put them to flight with heavy slaughter, then take spoils and continue the voyage toward the Black Sea.
III.Place and homonyms
Ancient geographers remembered a bay Amykos on the Bosporus; the name kept the myth attached to a real shoreline opposite Byzantium.
A centaur Amycus appears in Centauromachy lists; that creature is a separate atlas node (amycus-centaur). The Bebrycian boxer is the Argonaut antagonist alone.