According to the Hindu Succession Act which governs the inheritance and succession laws for Hindu, children of the deceased are class I heirs (sons and daughters on equal footings).For this purpose the your name should be present in the succession certificate. Any legal heir would be able to apply for this. The name of all the legal heirs and the their relation to the deceased is recorded in this and along with other documents a petition has to be submitted to the court of competant jurisdiction. The court will then issue a succession certificate under the Indian Succession Act.
Any document from ration card of that time to your parent’s divorce decree is enough to prove your relationship with that of your father. Birth certificate is important to get admission into school, that would also suffice for establishing you to your father. Then you can apply for a blood relationship certificate from the local muncipal or panchayat. It can be obtained by daughter, son, mother and wife. It establishes the relationship and would be a major proof document at the time of any dispute. It only takes one week to process in the local government office, if all the correct documents are submitted. As per the rules, it is under the State jurisdiction and as per the state the rules will change.
Reference: Hindu succession Act 1956