Mr. Dalmia has given valuable advice. Kindly follow it.
In a given situation employee can invoke the provisions of Industrial Employment Standing Orders Act, SE act applicable to the state, Payment of Wages Act, ID act as per explanation of employee under these enactments or approach civil court.
You may apply your goodwill, rapport, and persuasion, persistence, reasoning, negotiation, skills and minute the pending tasks/assignments and resolve the matter in your favor.
You may carefully look into the task/assignments on hand and exit formalities/exit format of your company and submit a written representation under acknowledgment addressed to good offices of your appointing authority, MD, CEO, Company Secretary and conclude that tasks on hand shall be completed by you within ………(say 7 days) and company should inform you in writing the designated employee for knowledge transfer, handing over the charge and company property by you immediately so that you can perform the task from your end. You may clearly mention the effective date of your resignation/last day in office in your notice of resignation. The contract can be terminated by employee or employer. In your case you are initiating the termination and you may mention that notice pay be adjusted in FNF statement.
You have posted that:
--“The new company is willing to buy out and they do not need a release letter.”
You may ask the current employer to adjust notice pay for shortfall in notice period ( basic+DA or as agreeable to you), encash paid/privileged leave, wages for the period you have worked, incentive etc, in FNF statement and affirm that if any amounts in correct FNF statement is payable by you shall pay the same by a/c payee cheque against a proper acknowledgment on the spot. Thus you shall get form16 as per FNF statement and as your new employer is buying out the notice pay, you shall not be subjected to double taxation.
--“They simply need my resignation mail which I have already sent and they are good with it.” Try and obtain an agreement even if by email or you may minute the essence of the agreement even if by email. Verbal committements may not rescue you in case of a situation.
You must keep your new employer on your side and in case last employer/HR becomes adventurous and barges into writing to your next employer to malign you, you may explain the situation in writing to new HR and ask them to forward their reply with a copy to you. You may charge the last HR/employer by name for criminal defamation. Let them drag their feet to courts at their expense.
--The clauses mentioned in appointment letter are conflicting. Employer on its own must not implement or push the penultimate and bad clauses. Al clauses mentioned in a contract even if accepted may not be legally enforceable. The craftsman who craft the appointment letter do include the inner wishes of employer knowing that majority of the employees may not muster courage to challenge them, and majority of the employees easily get subdued by tactics employers/HR use.
--“My HR is saying”. You may come out of saying and telling and better be in written mode and build record in your favor. This HR should acknowledge the receipt of notice and communicate their version in writing to you. You may demand acknowledgment and acceptance be supplied to you in writing.
--You may write to your employer to let you examine your personnel file maintained in their office and contest the adverse comments if any.
While in employment you may take out the copies of certified standing orders of the company (if any), leave rules, employee rule book, HR policy etc and all other relevant records which may help you later.
Although you have submitted resignation by email you may submit resignation by letter thru redg. post and narrate all incidences. On your last day you may submit final resignation citing effective date of termination of contract and notice of termination initiated by you.