Zeus is Kratos's father in the God of War series.
In the Greek-era storyline, Zeus is the king of the Olympian gods and the biological father of Kratos. Kratos does not know the full truth at the beginning of the series. The revelation becomes central to God of War II, where Zeus betrays Kratos and takes the powers that Kratos gained as the new God of War.
Their conflict expands across God of War II and God of War III. Kratos's anger toward Zeus becomes one of the main forces behind his war against Olympus. The games adapt the familiar Greek mythological name while creating a fictional family relationship specific to the series.
Ares is Kratos's former master and the original God of War. Poseidon and Hades are Zeus's brothers, not Kratos's father.