Generically speaking; The establishment may ask for certificate issued by 1st Class magistrate/SDM/competent court of law e.g; Distt. Courts..
Pls check with the establishment/authority and also at your location.
Hope you already have the Death certificates and legal heirs certificate of deceased father (your son) , mother, birth certificates of minors, …and other relatives shall issue the NOC if the need be for the purpose of said certificate..
If you are Hindu; then Mother is ClassI legal heir of son and Legal Representative/heir certificate issued for son should include your name and thus establishing relation with minor children(s) also..
In the meantime you may Go thru;
Guardians and Wards Act; 8,9, 10
For clarifications, in case of difficulties, and to get certificate from court, approach in person members of the family, competent and experienced well wishers, seasoned PIP, your community leaders , a very able senior LOCAL counsel of unshakable repute and integrity specializing in such/guardianship/Civil matters and well versed with latest citations, LOCAL applicable rules/laws/ … and having successful track record…. and worth his/her salt…..and share inputs /show the documents/evidence for a considered opinion..
At each location three are some counsels that specialize in such matters and they are well known.
Check for such counsels at LOCAL civil courts, HC, SC……