Joffrey in Game of Thrones always seems to believe that it is king's right that he can do whatever pleases him. He justified most of his actions by the same fact. However, he is always challenged for validity for his right on the Iron Throne. First, at the time of his coronation, Eddard tried to reveal the truth to everyone. However, Joffrey got him punished as traitor. That time, Joffrey seems to believe that his father's friend was trying to seize the Throne from him.
After that Stannis declared the same thing and started war against him. He also got support from the Southern Lords for same reason.
So, does Joffrey start believing that he is a bastard at any point of time?