Proof why I didn't serve notice period in previous organisation - Is it really valid?

I am right now working with IND bank and have been confirmed. 3 years ago, I was working with ax bank and without serving notice period i left the bank and paid whole amount to bank for shortfall of notice period. Bank issued me letter for same then i have joined Y bank where i worked and left same after serving proper notice period.
Today HR called me and said to me that 3 years ago you have left ax bank kindly provide us proof why you have not served notice period in that bank.
Is it really valid that bank HR asking for proof that too from 3 years ago because i have said about my family issues and they are asking for discharge certificate. while in between i have already worked with Y bank and they didn't ask same.

It seems to be a complicated case.
Normally BGV will be through before confirmation and not sure why your HR is asking some clarification on your previous employment, now.
However your Full and final settlement sheets can explain the payment of notice period etc.
So talk to HR with those papers and show confidence

You can talk to your HR and explain them about your clearance and full and final with payment in lieu of notice period which is completely correct if it is mentioned in your appointment letter and your X company is already accepted the same. Thus you need not to be worry and you can go forward and discuss with HR.