Did Poseidon have a child with Amphitrite?

No. Medusa was a Gorgon, who was turned into a monster by I think Hera.

pingo1387: actually, Medusa was a lovely young lady whom Poseidon was having an affair with. One day Athena caught Poseidon and Medusa making out and/or having sex in her sacred temple. Naturally, this pissed her off, so she turned Medusa and her two sisters into Gorgons.