Resignation can be without permission/notice. If option of notice pay in lieu of notice period is in service conditions then you may quote it. The employee can’t be held against his wishes. The employer may insist to serve the notice period if tasks are pending and employee is unwilling to indemnify the employer against any loss financial/or other that employer may suffer due to unfinished tasks.
If notice period stated in appointment letter issued to you is 3 month and no change in it is ever communicated to you and accepted by you then instead of remaining entangled with HR you should submit a representation to good offices of appointing authority, MD, Chairman………………….in writing under proper acknowledgment with a copy to you and you should obtain POD also.
In this representation you must narrate all representations made so far by phone, in person, in writing with dates, names, phone numbers and brief minutes of discussion, and conclude that no change in notice period was ever communicated to you and accepted by you, and you may also ask why your official email id is blocked (IN a smart language it should mean that you have been relieved?). You may mention that your career, employability is affected.
It shall be appropriate if such representations are drafted by your lawyer.
You may record the transactions with HR/Line managers (audio/visual).
You may approach a Labor Law consultants/Service Lawyers par along with copies of job advt, job application, interview call letter, offer letter, selection letter, appointment letter, CTC sheet, Salary Structure, Salary slips, STANDING ORDERS APPLICABLE TO THE ESTABLISHMENT (CERTIFIED/MODEL) AND EXTENDED TO YOUR DESIGNATION, HR policy, Service rules and regulations, Conduct and discipline rules, resignation notice, etc …………. Communications exchanged with company give inputs in person and proceed under the expert advice of your lawyer