The Catholic Church Is the Only Church That Even Claims Such Authority

There's no Protestant denomination that even claims this for itself. The closest thing you have to it are in some of the cults, as they're called,. These quasi Christian sects like Jehovah's Witnesses who claim to be the watchtower and the Mormons who claim to have the prophet. But even in those cases, where someone does claim to have some sort of authority, they can be easily dismissed.