Whenever you go for a document verification session in connection with a job or higher education, then your documents should match in all respect. Mismatch of fathers name is also an issue.
Now what you have to do is collect all the credentials of your father like his birth certificate, his Aadhar card, his PAN card, his driving license etc etc. Now check the name there. Is it same there or varying?
Now check your documents. How the name of your father is mentioned in them. As per the details provided by you his correct name is not reflecting in your documents.
One thing is you can go for a legal affidavit where all these facts are mentioned clearly and then it is to be signed by you, your father and then is to be signed by a court magistrate under his seal. Please remember that a copy of all the documents which are mentioned in the affidavit are to be annexed with it for the reference and they will be forming a part of it. You will have to take help of a lawyer for this.
This affidavit is to be kept by you and to be produced wherever there is an issue of mismatch of the father's name in your documents.
Knowledge is power.