Incorrect spelling in both 10th and 12th certificates.

Your mother's name is incorrect in your X and XII certificates. This will be a problem at the time of document verification so you have to approach your education board office and get it corrected. Check your mothers credential like Aadhaar card, Voter card, PAN card etc and give the copies of these as the reference for the correct name.

Sometimes the education offices delay in this and do not correct the certificates in time on one plea or other so better send the application for correction by registered /AD post to them with all the relevant documents. You will get the stamped AD back by post and keep it for reference.

Please write the correct name of your mother wherever you are applying and meanwhile contact a lawyer for making an affidavit in the matter giving all the details of this mistake in the certificates and attach the reference document copies which will form a part of the affidavit. This type of affidavit are in the nature of oath and solemn declaration and are quite common in the legal matters. This affidavit is to be signed in person by you and should be countersigned by a first class magistrate under his seal.

At the time of the document verification keep this affidavit for reference and for explaining the mismatch of the name of mother in the certificates.

It is always better to have the mother name correctly in all the certificates. You should get them corrected. First, you have to apply for correction in your tenth certificate. You have to apply through the school you have applied to the board. You have to attach a copy of a certificate in which your mother's name is correctly mentioned for reference. You have to fill the required application and attach all the certified copies as advised by the school administration and give it in the school. You have to take a xerox copy of the application and get it stamped by the school by the school administration as a token of your application submission in the school. They will forward it to the board and the board will take the required action. Once you receive the tenth certificate with the correct name, you can apply for correction in the 12th certificate. If you wish you can apply for both at a time.
It will take more time for the corrections to be made.
So as an immediate measure, you can try to make an affidavit. For this, I suggest you contact a known good lawyer in your area. He will guide you and see that the work is done. This will be shown to the employer when the certificate verification process takes place.

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 license 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.
The name,father's name surname etc., should be get verified even at the stage of collecting from school leaving itself as the same become base documents for the further studies as well for employment or anything.