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.