Hi

It is completely ok even if you don't have Sanskrit in your class 12 , you are still eligible for BA Sanskrit and can pursue it

This is because ,
to be eligible for BA Sanskrit it is not mandatory to have studied Sanskrit in class 12th. There's no barrier on subject which you have studied in your class 12th or the stream you are from

To be eligible for BA Sanskrit ,all you need to have  is 10 +2  qualification in any stream i. e Science, Commerce, Arts.

For example,
To be eligible for BA Sanskrit in St Xavier's College, Ahmedabad, one needs to pass 12th / equivalent in any stream.
And admission is on the basis of your marks obtained by you in class 12th board examination ,you can check the same by going through the link given below
https://www.careers360.com/colleges/st-xaviers-college-ahmedabad/ba-sanskrit-course
.
List of some of the colleges offering BA Sanskrit is provided below

St Xavier's College, Ahmedabad.
Maharaja's College, Ernakulam.
Government Victoria College Palakkad.
Government Brennen College, Thalassery.
Sree Sankara College, Kalady.
Atma Ram Sanatan Dharma College, New Delhi.
Ramadevi Womens College, Bhubaneswar

You can get the complete list by going through
https://university.careers360.com/colleges/list-of-ba-in-sanskrit-degree-colleges-in-india

Thank you