When Perseus cut the head from Medusa, there sprang from the Gorgon great Chrysaor and the horse Pegasus, twins of the same blow. He was so called because he was born hard by the springs (pēgai) of Ocean, and his brother for the golden blade (aor) in his hands. Then Pegasus left the earth, the mother of flocks, and flew away to the deathless gods; and there he dwells in the house of Zeus and brings to the counsellor god his thunder and lightning. Hesiod names Medusa's lover, who lay with her in a soft meadow among spring flowers, as the dark-haired Poseidon.2Hesiod — Theogony 278–286

Apollodorus and Hyginus confirm the parentage the Theogony gives: when Medusa's head was severed by Perseus, the winged horse Pegasus and Chrysaor, who would father Geryon, sprang from the Gorgon, and these she had conceived by Poseidon, whom the Latins call Neptune.3Pseudo-Apollodorus · Hyginus — Bibliotheca 2.4.2; Fabulae 151

Ovid, telling of the same beheading, sings that the spilt blood of Medusa gave birth to winged Pegasus and his brother together, twins of rapid wing.4Ovid — Metamorphoses 4.785–786

Hesiod sings that the Chimera — a thing of three beasts, a lion in front, a fire-breathing goat in the middle, a serpent behind — was slain by Pegasus and noble Bellerophon. Apollodorus tells how it was done: Bellerophon mounted the winged steed, the offspring of Medusa and Poseidon, and rising on high shot the monster down from above, when Iobates had set him the deed that he might perish in the attempt.5Hesiod · Pseudo-Apollodorus — Theogony 319–325; Bibliotheca 2.3.1–2

How the wild horse first came under a rider, the Corinthians told to Pausanias: at Corinth stood the temple of Athena Chalinitis, the Bridler, for of all the gods it was Athena, they said, who most helped Bellerophon, and she herself broke in Pegasus and bridled him and gave him into the hero's hands.6Pausanias — Description of Greece 2.4.1