Euphemus was the son of Poseidon and is sometimes portrayed as the son of Europe. Europe was the daughter of the giant Tityos. Tityos was the son of a mortal princess named Elara and Zeus. He was not a good guy and got sent to Tartarus and sentenced to the Prometheus treatment during his stay.
Anyway, Euphemus was maybe married to Hercules’ sister, Laonome. His marriage to her changes depending on the source. He could walk on water and was pretty much perfect. He is not, I repeat, is not, the same Euphemus that was killed in the Iliad.
Euphemus isn’t known for much, except winning a chariot race at the funeral games of Pelias and starting the civilization of Cyrene in Libya. He met up with his half brother (on Poseidon’s side) and was given a dirt clod as a gift of hospitality (the Greeks were really odd about Hospitality). He was supposed to drop the clod in front of the Underworld, but it got washed overboard and through some really odd, kinky dreams about sleeping with one of Triton’s daughters while crying about it and nursing her, he gave birth to a civilization. The clod grew into an island called Thera, and Euphemus’ descendants ruled there.
The Greeks were fricken weird sometimes.