Is pegasus the son of Poseidon?

In some versions of the myths, yes, he's the son of Poseidon and Medusa.

What I read is that he 'sprung' from the body of Medusa after she was slain by Perseus, the son of Zeus.

Medusa used to be a beautiful maiden. Poseidon and Medusa were found together in the temple of Athena by Athena. Athena found that deeply disrespectful, and since she could not punish her uncle, she settled for turning his new girlfriend into a hideous monster.