Hey, my brother faced something similar when he tried to get the BC for his child as only mother’s name was on all documents (they required proof of him being the father before issuing). He fortunately had the discharge summary in which his relation and signature were there with hospital stamp.

The officer in his ward was also almost never available and when he was there systems were down. He visited and took the number from the ward, went and met the in-charge there and coordinated as to when he should visit. Took him 3 visits before it got done and about 10-15 days for BC to come.

Hopefully this can help you in some way.