Options to getting early relieving with employer

Approach avery able counsel specializing in labor/Service matters.

Your counsel after considered examination of facts,docs on record may opine that notice period of 60days is applicable in your case or not, even if inserted in appointment letter.

If you are coverd by variosue nactments then it may not neccessarily apply.

As the HR person you should be in the know of the norms followed by the company. The question is how far they are in consonance with public policy. Any suggestion is possible only if material facts are known. 

The medical leave during notice period should ideally be not denied.

However the employer may cite T&C of Leave POlicy and/or ask medical certificate.................

The private leave policy should provide superior benefits than applicable enactments.

It is indeed required to examine the coverage by enactments in your case.