What is the ruling on swearing by the Mus'haf in the mosque to clear oneself of an accusation of theft, and what is the punishment for the liar?

If a Muslim is accused of a reprehensible act they did not commit, there is no impediment to them clearing their name before people, whether by a simple oath or a reinforced one, such as swearing on the Quran on Friday in the mosque, as long as they are truthful and innocent. This is not among the forbidden types of idle talk, because it serves a legitimate purpose. As for swearing a false oath, it is a great sin and a submerging oath (yamin ghamus), which plunges its taker into Hellfire or sin, and they must repent sincerely.