Hello Yash, 

For correcting your Father's name in both 10th and 12th marksheet, first of all you must go the the school from where you pursued 10th and 12th, contact the principal or the administration of the school. You will be provided an application form to fill for the correction that you need to do. 

The institute might ask your all the documents like school leaving, passing, marksheet, tc, etc. 

They will then forward your request to the board and it might be soon informed to you when your papers come. 

Or, you can file an affidavit before the executive magistrate with a proof that the corrected name is your father like Aadhaar card, pan card, etc. 

Good luck!