These are minor mistakes that can be troublesome at a later date. For all competitive exams and jobs, you will be filling up online application forms and later submit the documents at the time of document verification just prior to the final job interview or joining the post.
If you have given the details correctly, then this error can be the mistke of the school/college while send the details to the board or university. But it is difficult to ask them to rectify.
You need to have formal proof of your mother's name. Her PAN card or Aadhaar card, passport or Caste certificate if any can be used as the proof of her identity.
If you do not have an ID document with your mother's correct name,then you would need a formal/legal affidavit stating her correct name. This can be sorted easily, please contact the Notary in your locality or Civil court areas. After this, approach the local newspaper office (one English, one regional) and publish the correct name of your mother ( this is done regularly by newspapers, so no need to worry about procedure).
Once you have either of them, then draft a letter to the principal or dean of the 10th and 12th school/college stating that you intend to correct the name spelling mistake related to your mother's name.
This letter will be forwarded via the school to the respective state boards of 10th and 12th.
You will need to pay a small standard fee for the same. It takes about 30 days to get the correction done. Some state boards offer a urgent/priority service for a higher fee and release the document in 10-14 days.
The corrected certificates will come to the respective schools, so please retain the acknowledgement number or the payment receipt for future correspondence in case there are delays.
If you have done your 10th and 12th via CBSE, then the process is the same except that CBSE will insist on an affidavit and newspaper advert regarding the change/corrrction in mother's name.
