Management wants an employee on medication to pay 15 day salary/ serve notice period

Hi,
I have given my resignation & serving a notice period of 15 days. I have been working since 8 months, have not received letter of confirmation eligible after 6 months. I have resigned for health issues and serving a notice period of 15 days as I have to leave to my native place for further treatment. The management has responded to my resignation mail after 8 days requesting me to serve full 30 days & discuss with them further. I had a discussion later on and the director has asked me to give 15 days salary as compensation to them or serve remaining 15 days also. Am I liable to pay the compensation as I am not yet a confirmed employee? Also, the director has threatened that he won't give me a relieving letter or a clean chit if I leave in 15 days. Does the company have right to do that?

Dear Aparna,
Whether 30 days of notice for resignation was mentioned in your appointment orders? If so either you have to serve the entire notice period of 30 days or pay for the remaining unserved period of 15 days.