Hello Student,
There is nothing to worry about, apply for the JOSAA counseling. The moment you get a seat allocated, there is a process to get the documents verification, you will be provided with the information about the center (closest NIT/ IIT from your place ). At that time bring this issue to the concerned verification authority at the allocated center. They will ask you to furnish Notary certified affidavit, In this you have to state that the father's Name written on the Admit Card, and your Father's Name (correct version) are the same person.
In advance get the Notary certified affidavit ready from some local Notary, and submit at the documents verification center . This will save you from the last moment rush.
You can update father's name on Aadhar Card easily near any choice center of your locality. As it will be beneficial to you. But there would not be any issue if you're alloted a seat.
Thankyou. Hope this information helps you.

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