There is a lease? One you signed? If so, you should’ve probably kept the keys to the agreed upon date. You handing in the keys was an informal forfeit. You can try and get a lawyer and try to get some money back since essentially landlord is double dipping but that will probably depend on when the new tenant’s lease was signed and their agreed upon date. You’re going to have to decide of the lawyer fees are worth the gamble and the money you’d get back. This isn’t legal advice, I’m not a lawyer.