Notice period issue

Hi, I work for a Tech company in the senior capacity (AVP) I joined this company 15 months ago. They issued me an offer letter which doesn't mention anything about notice period or salary payable in lieu of notice period. I signed the same and joined the company. Company has not issued any Appointment letter or Confirmation letter subsequently. I haven't received or signed any document other than offer letter. I resigned on 1st June by sending them an official mail. Gave them 30 days notice. Company has not responded formally to that till today (i.e. 16th June) Around 13th I was called for verbal discussion and was asked to reconsider. I have refused to do so and also sent a mail stating that I would like to go ahead with my resignation. Now they are stating that I am at the senior level and that the notice period should be 90 days. It is difficult to find replacement etc. My question: Can company specify notice period after I have submitted resignation stating that it is implied at senior level? Can they create issues by withholding my relieving and F&F