1. Request an early release without payment then if it does not work;

2. Ask the new company if the can buy you out, if does not work;

3. Then you have to pay for the balance.

You can resign all you want even 24 hours, your boss need not to accept or reject so long as it has been communicated that your desire to terminate the contract, and it must be with proper notice or payment in lieu of notice, otherwise you may get sued for breach of contract.