I honestly think you should check with the labor law by going to the office and ask before you make any drastic decisions. Usually when you sign, meaning you agree on all the terms and condition set by the company. 3 months without buying out, means cannot. Now not a time to seek if is a norm or not since you have already agreed.

If the company insist on wanting you to serve the entire 3 months, you only can accept it. But I don't know why they want you to serve 3 months. You can practically do nothing there and yet they need to pay you.

Try to delay the starting of your new job.