If your father's name is the same (shortened) in your educational certificate AND proof of Identity (PAN,Aadhaar,DL) and caste certificate (if applicable), then you would not have any issues.
If you find a mismatch, then it would be better to align all your certificates and documents so that you do not have any issues when you apply for Government jobs as most of them would be online and there should not be a mismatch at the time of document verification. It would also be useful to rectify it before you apply for passports so that you would not have issues with mismatch and visas, international job offers/deputation etc.
I would suggest, why risk a chance and face issues later, any way you are in your final year and still have to get your B Tech degree certificate.
10th and 12th certificate correction
You can get father's ID proof (PAN, Aadhaar) that has his correct name. Please get attested copies of father's ID and then draft a letter to the respective boards (10th and 12th) requesting correction of father's name and issuance of a new certificate. Please forward this to the respective boards via the school prinicpal or head of institution of 10th and 12th. There would be a small fee applicable and in around 4 weeks time the board would send the new certificates to the school/12 college.
Please inform your College office and the university officials about the proper father's name so that your degree certificate and consolidated marks card is issued in the future with the correct father's name.