This depends on where in the play you are referring to. He is always paranoid that he killed his dad. Oedipus is also frightened of the King of Corinth, who he believes to be his father. He is not afraid that the King will do HIM harm, but rather that he (Oedipus) will do harm to the King. He is worried that the oracle's prophecy will prove accurate and he will kill the King of Corinth. The irony, of course, is that his father is Laius, not the Cornithian king, and he has already committed to preordained murder.