It is one part of a "magic folding quarter" It consists of two pieces with a rubber band in the groove around the coin.
I say yes to part of a magicians folding quarter.. but yours seems to be just on one side. They are usually 3 parts. So there are 2 different tricks.. the 3 parts quarter to fold and stick into a bottle - Then there is a 2 part quarter.. the one you have was made to look like you took a bite out of it. You would blow on the coin then it would restore itself. the quarter you have lost the other piece. Your Quarter is not a Mint Error coin.
