If the passport authorities are instructing you to furnish birth certificate, you may have to first approach the Municipality with an application to issue the same.
If the municipal authorities express that there are no records available in their register about the particulars/details of your birth then you get a non availability certificate and then apply for a direction in a private case before the jurisdictional judicial magistrate court , to direct the Municipal authorities to register your birth in their register as per the details you have furnished relying upon substantial documentary evidences in your possession, produced before court.
After this process is completed you may approach the municipal authorities with the court order and obtain the birth certificate accordingly.
After that you can apply for re-issue of passport with correct date of birth as per the birth certificate by enclosing a copy of the birth certificate.