Did Poseidon have any relationships with any gods?

yes.

Poseidon's brothers were Zeus and Hades. His sisters were Hera, Hestia, and Demeter.

well known children of Poseidon include the hero Theseus and the merman Triton.

Poseidon also had a "romantic" relationship with Medusa, but i believe this was before she was turned into a monster, and also the reason why she was turned into a monster. I should add that by romantic i mean she was raped by him, which for a male greek god was normal.

Like most of the male greek gods, Poseidon had many lovers and had many children with these lovers. His wife was Amphitrite, and she was a nymph. He also once hooked up with his sister Demeter.

Most of the greek gods were related, and inbred.