You have your father's name mismatch in your marks card and the rest of the documents. Please check what your father's correct name is, along with your initials. If it is only the 10th and 12th, you can change it easily.
If the rest of all your important documents carry the wrong name/mistake of your father's name, you have change all of it.
Now all the records are updated digitally, many application forms for Government jobs are all online. If you have errors with fathers name, your name, date of birth etc, now is the time to change it because, it could be a potential issue at document verification and future legal documentation. These things take time which may not be available for you once you actually need the documents for verification , joining etc.
Please check you caste certificate and Driving licence too, if you have them
For changing the father's names with the board it is a little tricky. If you have filled the forms correctly but the school or board has made the error, then you can approach them with evidence.
If not, you have to carry documentary proof that shows your father's name clearly ( like your father's Aadhaar card, PAN card, Passport, RationCard etc) and get it corrected.
You can draft a letter yourself, enclose attested copies of your father's correct name and submit it to the board (10th and 12th) by forwarding it through the respective school/college principal. If it is a CBSE certificate then you need more documentation.
Like a correct name affidavit from a Notary, father's name change being published in two news papers, fees, letter from school stating what is the actual name recorded at the time of admission and the forms forwarded via the principal to the CBSE board.
If you have to correct the mistakes of your father's name in PAN,Aadhaar,Voter's card etc. The process is similar and the name correction forms are available online or you can get if corrected at the local government centers that offer government document services.
Link for further information of name change in CBsE:http://cbse.nic.in/faq/revised_dob_name_corr_rules_2015.pdf