Hello Student

Aadhar card is more important document than transfer certificate in which your father's name has been mis spelt. So to fill up any kind of form for admission or registration you should use the name of your father written  in Aadhar card. And you should immediately correct your father's name as it has been written in your admit card of 10th class examination by an request application to the authority of your school. After getting the TC  where your father's name is it as it is  in the admit card or hall ticket of your 10th class and 12th class examination then it is okay. By this correction you may make correction the name of your father as if mistake  in the Aadhar Card if there is any mistake.

This will help.