Resigned During Probation but HR Wants Me to Stay 3 Months—What Should I Do?

Hello, in my current company, I'm in the probation period and recently resigned from my job. As per my offer letter, during the probation period, I don't have a notice period, and HR confirmed this in a written email. However, my HR Officer is not accepting my resignation and is asking me to serve for 3 months. Please help me with how to approach this situation.

Borrowing one line from your post - "But my HoD is not accepting to relieve me and is asking me to serve for 3 months."

Presumably, HoD means your Head of Department. What does your appointment letter's Separation clause say about it? Please refer to the same. (Always refer to your Offer of Appointment's Separation clause instead of the Job Offer letter regarding notice period intimation).

If your Appointment order states that during the probation period, no notice period is required to be served, then you are not legally bound to serve a notice period.

But, if your HoD says that he cannot relieve you unless a suitable replacement is given to him, HR cannot do anything.