Supreme court has given verdict log back that it is not necessary to mention fathersname in school enrolment.
You will remain child of your biological father despite your mothers name everywhere. So how does it matter?
Only you have to produce proof to that effect. Even a child born out of wedlock is also entitled to inheritance in Indian succession act or hindu succession act whatever.
Apply to a local court to get your certificate amended. You mother will give evidence with some other proofs.
Not a really big issue.Relax