Please review your appointment letter.
Read the relevant clause carefully.
In my opinion, work for 30 days and receive 30 days' pay in lieu of notice if the employer is not prepared for that, follow these steps:
Inform your boss that you will serve the required notice period, obtain acceptance of the resignation (do not specify your last working day).
Do not disclose your new company's name. Receive your last month's salary, stop going to the office the next day, and inform them that you are advised bed rest by a doctor. Provide a doctor's certificate.
In the new company, state that you have a resignation acceptance letter, and the full and final settlement will be completed 45 days later when you receive the relieving letter as well.
If the old company contacts you, explain that you cannot attend the office due to illness. Request them to consider your last working day for relieving purposes. If they insist on a payout, inform them that you will make the payment once you receive the relieving letter. Do not make the payment initially. Ask them to send a scanned copy of the relieving letter for verification before visiting the office to collect the original letter and provide a cheque.
Regards,
Anirban
9768278408