Harry Potter: Echoes of Destiny

After dying in our world, Corvus is reborn into the wizarding world as the secret son of Regulus Black. Blessed with knowledge of what will happen in the future, he tries his best to hinder Voldemort to gain power, getting more powerful himself and perhaps to fulfill something, that was predestined for him.

The story starts at the beginning of Book 4.
Hogwarts starts at 13.