No. He is an offspring of the Titans Cronus and Rhea. Gaea would be his grandmother, though.
Rhea was the mother of Poseidon, and Gaea was her mother, so Poseidon's grandmother as well.
Gaea never married: she mated with Ouranus to produce offspring including the Titans.
Cronus and Rhea, the father and mother of Poseidon, were siblings, the son and daughter of Gaea and Ouranos.
Daughter of Gaia ( also spelled Gaea ) and Poseidon
Uranus, the first ruler of the universe, god of the sky and mate of Gaea, the mother earth was Poseidon's grandfather.
Gaea is the offspring of Chaos, sometimes from a union with Nyx.
Kronos was a TITAN, this meaning he was the youngest offspring of Gaea (Earth) and Ouranos (Sky), it was he who castrated Ouranos his father. With his sister-wife Rhea he had six children: Hestia, Hera, Demeter, Poseidon, Hades, and Zeus.
The ancient Greeks believed that earthquakes were caused by Poseidon, the god of the sea, who was often associated with natural disasters. They thought that earthquakes were a result of Poseidon's temper and his use of his trident to shake the earth.
Well there was a smithy race of Cyclopes whose parent were Gaea (Mother Earth) and Uranus (Father Sky), they were bound in the Underworld by their father for their ugliness, but in later myth Poseidon was the father of the Cyclops, Polyphemus, who Odysseus killed.There is more than one cyclops, and they have different fathers. The original three Cyclopes were sons of Ouranos (Uranus) and Gaea. He was so appalled by his offspring, and fearful of their great size, that he imprisoned them in Tartarus.The other well known Cyclops was Polyphemus, the cyclops shepherd that trapped Odysseus and his crew, devouring them. That Cyclops was an offspring of Poseidon.
The Titans
the Kraken could be summoned by Poseidon. but I've also read that it could be summoned by Hades and Gaea. this is what i know; The Kraken was created by (Poseidon, Hades, Gaea) so that the god's could defeat there corrupt fathers the Titans. After which, Zeus became King of the Gods, ruler of Olympus, Poseidon became ruler of the seas, and Hades the ruler of the underworld.
Gaea is the mother of Rhea and Kronos, mother and father of Poseidon and goddess of the Earth, the consort of Gaea was Ouranos. Mythology does not tell a location that Rhea and Kronos were born.