1.if there was no mentioning of notice period then the college cannot force you to give 2 months salary as notice period.
2.However beofre quitting you were supposed to give them reasonable notice to quit like one m0nth or week.
3.anyway f they do not agree then send them a legal notice seeking your due.it should work.
4.FIling of any case is not suggested as your career would be tarnished by their false propaganda,