Some people claim that their god is omniscient. I am inclined to claim their god is non-existent. Now, strictly speaking, there are two ways to take a claim of omniscience. One is that the being knows everything that will ever be of consequence to us. The other is that the being knows everything period. The first is possible (though highly doubtful.) The second is not.
Consider the statement "'does not produce a statement that god believes when preceded by its own quotation' does not produce a statement that god believes when preceded by its own quotation." I realize it's a mouthful. I believe it is a true statement because I do not believe there exists a god to believe that or any other statement. But suppose there is a god. If he believes that statement, then it is false. A god who believes a false statement is not omniscient. Well, suppose he does not believe it. Well, that is just what the statement says; and so we have a true statement that the god does not believe. He may or may not actively disbelieve it. Either way, he is not omniscient.