Son of the Moon, Master of Swords

After his contract with Alaya is over, Shirou Emiya, aka Archer, is sent into the cycle of reincarnation after being told that his beloved Artoria Pendragon did the same while waiting for him. He is reborn into a new world due to a very powerful being taking him away from his world and planting him in its homeworld. Archer is then reborn as the son of the most unexpected woman in the entire multiverse: Artemis the goddess of the Hunt and Moon. He is named Perseus by his mother and left on the doorstep of a dear mortal friend of Artemis's as his biological father died in a car crash the night of Percy's birth. When Percy turns 16, after the Titan War, he is found by the satyr Grover Underwood and is claimed during his first game of Capture the Flag. What happens next? Well, only Chaos knows.