Between any employer and employee, appointment terms act as a binding agreement. If as per your appointment terms, either you or your employer can terminate the employment with a notice or pay in lieu of; then you have to serve a notice or pay for it. The other way is to have a mutual agreement with the employer and request for a notice waiver.
Considering all you mentioned, i suggest you assertively talk to the management and sort things out rather than getting into a conflict.
From India, Delhi