Gift deed

While the property is mortgaged, you cannot transfer the property until the mortgage deed is released.  Is the property your self or ancestral?

The issue depends on the facts of the amount borrowed and purpose.  In fact, gifting a property when it is under mortgage amounts to conversion to avoid borrowers and for alienating to your own daughter.   But in your given case, you can specify the NBFC mortgage in the gift deed and can state that it is your responsibility to clear the mortgage from NBFC and get a clearance certificate from NBFC.  There is nothing wrong if the facts of mortgage are stated in a gift deed.  However, remember that NBFC is having first charge, and only after getting clearance from them your daughter can get exclusive rights on the gifted property.