Oncius was a demigod and a son of Apollo.
Oncius was a son of Apollo and a ruler over Oncium, a region of Arcadia adjacent to Thelpusa as well as eponym of a city Oncae. He owned a herd of horses, in which Demeter tried to hide from Poseidon's advances, changing herself into a mare. Poseidon did mate with her in the shape of a stallion, which resulted in the birth of the fantastic horse Arion. Oncius kept Arion and later gave him away to Heracles as the latter was starting a military campaign against Elis.