Who were the children of the Greek god-Poseidon?

Poseidon like many Ancient Greek Gods, had countless affairs with mortal woman producing countless Demigods offspring.

Poseidon also had many affairs that produced many Cyclops children the most famous one being his affair with Thossa. This produced the Cyclops Polyphemus (he is best known for his role in the story of Odyssey)

Poseidon married Amphitrite.

She was daughter of Nereus and Doris.

Nereus was an early deity, known as the Old Man of the Sea.

Doris was the daughter of the titan Oceanus.

Poseidon and Amphitrite had three children.

Rhodes (the Island of Rhodes was named after)

and Triton (he became Poseidon's herald and successor).