Atreus is the son of Kratos and the second child of the Spartan overall. However, the first child of Kratos was killed by him in Greece due to foul play by Ares. His second child is his only one and appears to be just before puberty in the soft reboot.
Throughout the game, the story is mainly about the coming of age process and being a father for Kratos. Because of Kratos's bloodline, as his father is Zeus, Atreus is also part god.