You are expecting a dispute, therefore tread carefully and leave no chance of error at your end. Take the help of elders in the family, experienced and competent well wishers, lawyer/law firm and submit communications structured carefully to suit you, for your transactions with both the employers, and build record in your favor.If HR is not agreeing you can seek an appointment with your appointing authority,MD/CEO,HR Head,and request their good office to help you.
Some of the Govt. Organizations are rigid on getting relieving letter, and if you do not submit all the documents asked by them, they may ask you to give up the govt. job. Therefore it shall be in your interest to obtain list of documents to be submitted by you, and explain before hand which documents you can submit and which one you can not.
Take your next employer in confidence and explain the situation, in person and followed by a written request. You can mention that your present employer is not willing to relieve you and has stressed upon you that the relieving letter may be blocked if you do not comply with their order to complete the notice period i.e. up to dated.......
You can mention that you are contemplating to surrender notice pay for the shortfall in notice period, in your F&F, and request the next employer to absorb you on the strength of copy of your notice of resignation, resignation letter, and proof of dispatch e.g. receipt of redg. Post/ speed post. You shall be able to submit F&F, service certificate, upon receipt from the past employer.
Take your manager in confidence, complete all tasks on hand and obtain email/letter etc from your reporting authority that you have completed all tasks, and nothing is pending to be done, by you. Submit all company property and obtain receipt and comment nothing is due towards you. Both of these may suffice as NDC/NOC. You should write to your employer that you are willing to cooperate to transfer the knowledge and you should be informed in next 3 days to whom you should do so. If your manager indicates you can train the designated employee and put it on the record that you have transferred the knowledge and also obtain an email/letter from the designated employee or your manager. You can inform the company say 7 or 15 days in advance by a letter addressed to your appointing authority, that your effective date of resignation shall be dated………..and company should make the arrangements for smooth exit and during this period you are willing to cooperate and you should be informed for any help expected from you, sufficiently in advance. Ask the company to supply you your acknowledgment of resignation, acceptance of resignation, F&F, settlement of a/c and proceeds, service certificate, form 16, PF accumulation reports, PF transfer/withdrawal reports, NOC/NDC, last salary slip etc….. Within dated……..(as suitable to you)
You can prepare your own a/c of payables by you to company and receivables by you from company (F&F according to you. Include amount equivalent to earned leave) and you can mention that the shortfall in notice period equivalent to Rs……..may be deducted from your F&F, and ask the company to revert to you for any advice on this statement or any corrections to be done. If the company disagrees you can always submit notice pay by an a/c payee cheque/DD (keep a photocopy), along with covering letter under acknowledgment, by regd/speed post, followed by email.
Service certificate can not be blocked. Company may block reliving letter. If you feel that past employer, or HR, is stepping on your toes, and is rigid and adamant, and which may spoil your future prospects, you may visit o/o labor commissioner, and meet labor inspector also and lodge your grievance. Id deemed fit you can issue a legal notice from your lawyer. This should solve your matter.