YOu have found a mistake in your 10,12 markscard. Please check the correct spelling of your name, initials and your father's name and take this chance to check on whether it is just these two marksheet or other documents(including caste certificate if applicable) also have spelling errors.
Earlier, most jobs used to accept the degree certificate and class written on it. Now many jobs have a cut-off of 55% etc, hence the marksheet becomes more important. Most applications would be online and employee roll also would be online in most offices. It is relavent that the spelling and other details (date of birth) etc are correct so that you have no issues at a later date.
Now, for changing the certificates, you first need to make a affidavit with your correct name done by a Notary. Once this is done, then you need to publish your correct name in two newspapers ( one English and one vernacular language). Preserve the originals of both.
Then apply to the state board with these evidence along with a covering letter stating your request. This application/request is forwarded through the school pricipal to the relavant state board. You may need to pay a small fee that would be applicable as per the state board regulations.
If you have erros in your other documents, please get them corrected so that when you join the bank, you will have all the details in order.
You mention that you are due to join very soon, if you have cleared your bank exams and are waiting for your document verification, you can explain the truth to the authorities as to the oversight of the mistake and the new documents can be produced.