Percy is a demigod.

His mother is human, his father is the Greek god of the Seas. Percy has been a demigod for the last thirteen years, and he is rather good at it. Completely coincidentally, Percy has also been remembering a whole other life for the past thirteen years but shhh don't tell the Fates that. You're not supposed to bind two threads of life together, after all.

OR: Perseus Jackson, a transmigration of the soul done wrong, and Ancient Greek tragedy that is all too present.