Since the notice period for termination of service is 3 months, you are supposed to give 3 months notice and not 15 days notice. After giving the 3 months notice and if you want to leave after working for 15 days, you can then pay 2.5 months salary as indemnity for the short notice.
i) The company can disagree you last day, so can you.
ii) You are not covered by the EA.
iii) The company cannot physically hold you back, if you decided to leave by paying the required indemnity.
iv) If the company wants to sue you for some reasons, it is up to them.
That's my view.
Since you are not covered by the EA, you can consult the local Industrial Relations Department and get advice as to what exactly you should do. Get their official advice will be better.