Validity of Affidavit for name correction in graduation degree

Name,father's name,Date of birth are the basic details which required till our last breath for anything to be proved and they should be similar and a correct one in all documents. The school certificate for seniors and birth certificates for youngsters become a valid one. As the date of birth is deciding matters in one's life till his end,much care should be taken in the beginning itself. School certificate,college certificates,aadhaar,Pan card,voter Id, driving licence should tally each other. You immediately approach in person to the college authorities and get corrected. No correspondences will yield good result rather than personal approach. Your delay will make the matter more delay.
In your case no affidavit is required unless otherwise specifically asked by the university authorities. However your personal approach with necessary documents solved this matter easily.

What about your SSC and Intermediate certificates. Are they correct? If they are correct with respect to your father's name there is no necessity of affidavit. During the verification, they may nor object as the name is correct and no surname. Your name is having the surname. So they will not reject your application for this reason. Worst comes to worst they will ask you to submit corrected certificate before you join in the job.
But it is better to get it corrected. Apply to the University through the college you have studied. You attach your birth certificate or SSC certificate or Intermediate certificate copy to your application. They may forward it to the University or they may ask you to go to the university directly. You can contact the university and they will get it corrected.

Your document verification is next week and now you have found that your degree does not have your father's surname.

What is important is the details you have entered in the application form while filling up at the initial stages. Then what your other documents of education and proof of Identity shows. If all the documents you have and the application form does not have your father's surname, then there is no issue. In case there is a discrepancy with some mandatory documents with and without, then the verifying authorities will ask for explanation.

Since you have only one week, you cannot get it corrected. What you can do is gather valid documents of your father that has his correct name. Then you approach the local Notary for getting an affidavit that states your father's correct name. Please also include the statement that the person with both names and one and the same.
After this publish the corrected name in two newspapers ( one English and one vernacular language).
With the above, you have legally accepted evidence of your father's name.

If questioned, please show the above and explain to the authorities about the minor error and that you will rectify the certificates soon. They would oblige as there is not major facts altered or hidden.

Please check your Xth, XIIth, AADHAR Card and PAN Card. Is your father's name mentioned correctly in those documents? If yes, then there would be not much problem for you. You sign an affidavit before the first class magistrate of your city and submit the affidavit at the time of document verification. Later (after job verification), you have to publish similar advertisement in an English and in a vernacular newspaper. The affidavit before a first class magistrate and original advertisement must be preserved permanently.