Birth certificate is not necessary for issuing caste certificate you just need one thing if the caste of your father is under the category whatever the states he belongs to then you can issue it from tehsildar of your district you need to take following documents for issuing caste certificate.

1.Proof of identity (Aadhar, PAN, Ration Card, Student ID etc)

2.Proof of Address

3.Community certificate of either parents or siblings.

4.Self declaration.