Misspelled name in certificate

From your narration, it appears that the name of your mother is incorrect in your 10 mark sheet. If it is so then you have to apply to your education board office for correcting the same.

For this, you have to give copies of support documents where her name is correct. For example Aadhar card, Voter card, PAN card etc.

On the contrary, if her name is correct in the 10th mark sheet but not correct in the 12th and graduation then you have to go for correction in these documents by the respective authorities following almost the same procedures. Some institutes charge a fee also for this work.

Alternatively, you can go for a legal affidavit by consulting with a lawyer. The affidavit will spell out these details and the copies of supporting documents will be attached to it. The affidavit is to be signed by you and countersigned by a first class magistrate under his seal. In some places, the court insists for publishing the brief of this correction in the newspaper also. In that case that is also to be complied with.

Your mother's name is matching in 10th and 12th certificates. But which is correct you have not mentioned.
If your mother's name in 10th is correct and it is wrong in 12th, the correction can be done easily. You can apply to the board attaching your 10th certificate copy and asking for the correction. You can do that through the school in which you have studied. Then they will forward it to the board and the board will correct the same and send back to you through the school again.
If it is correct in the 12th certificate and it is wrong in 12th, it requires some more additional supporting documents. You have to again apply to the board through the school. But you have to attach a proof of your mother's correct name. If she is having her 10th certificate in which her name was mentioned correctly, you can attach a copy of that certificate. Then you can also attach a copy of a valid document like your Passport wherein the name of your mother was correctly written. By attaching the copies of these documents you can apply.
If both are wrong, first you have to get the name corrected in 10th certificate following the procedure mentioned above and then the 12th certificate as mentioned above for 12th certificate correction.
These processes may take a little more time. So to have a valid document at the earliest you get the affidavit made. For the process of making this document, you can contact a good lawyer in your area who will guide you accordingly.
It is always better to be proactive and get the documents corrected so that we will not lose a good chance because of this mistake.

Name of mother in school certificates do not have much importance in many places but if they entered once it should be correct in genuine and if there is any mismatch or incorrect spelling it should get corrected immediately.
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.