What were the names of Poseidon children?

Answer 1

Poseidon like most of the other Greek Gods had many Demigod / Half-Blood children with mortal women.

Poseidon and his wife Amphitrite had three children.

Benthesicymen, Rhodes (the island of Rhodes was named after him)

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

Answer 2

Poseidon had many children: gods, demigods and cyclops. But his most famous one from each kind are Triton (god), his heir and son with his wife and goddess, Amphitrite; Theseus (demigod), the first to navigate their way out of the Labyrinth; and Polyphemus (cyclops), the cyclops that Odysseus attacked on his journey.