Yes, mortal men and women can worship Poseidon.
To be a god.
Amymone's son by Poseidon was called Nauplius.
His mortal sons were Theseus, Pelias, Neleus and Hippothoon.
A demigod is half mortal and half god, meaning one parent is god and one parent is mortal. a demigod of Poseidon is a demigod with Poseidon as his/her father and a mortal mother. an example of this is Percy Jackson in the "Percy Jackson and the Olympians Series" By Rick Riordan
there is not record of Poseidon ever having any mortal daughters (half bloods ) at all ,his female offspring were either imortal,nympes,giants and even animal's mortal children were men....
When they wished.
He was the son of Poseidon and a mortal woman.
Triton, Athena, Despoine, Proteus, Aiolos, and Asopos are Poseidon's children. Poseidon also has nymphe, animal, giant and mortal offspring.
The Greek god Poseidon had a mortal brother named Theseus. While Poseidon was the god of the sea, earthquakes, and horses, Theseus was a hero and king of Athens known for his adventures, including slaying the Minotaur. Their stories intertwine, as Poseidon was said to be the father of Theseus, highlighting the connection between the divine and mortal realms in Greek mythology.
34: see link below.
They are forbidden to have children with mortal women.
As many immortal/mortal/demigod daughters as Poseidon has.