You need to take the following legal steps:
1) File a Civil Sut for Declaration of date of birth of your child with proper reason for past mistake in dob
2) In the civil suit, implead the GHMC commissioner and Regional passport officer as a defendant No.1 & 2 and make "All concern" as defendant No.3
3) Normally, the official respondents will remain exparte and paper publication is ordered by the court for all concerned.
4) Once the suit is decreed, approach the Government press, Chanchalguda, Hyderabad for notification as prescribed by them in specified format
6) After publication, contact any passport agent for rectification of name in the passport
Best wishes for complying such lenghty procedure on your ow