Hi

You won't face any problem . Even if you drop out in the middle of your graduation then the colleges don't return your 12th T. C as it has already been used for admission in their college, they provide you T. C of their own college when you leave it.

Now that you want to get admission in BA, it's completely ok you can submit your college bsc T. C also it doesn't matter even if the two colleges are under different universities

††††Personal experience :- I have friend who was doing bsc from Ranchi university, but he found bsc tough and didn't even attend the semester exams due to which he failed. Then collected T. C and got admission in B. A in Vinoba Bhave University i.e in a different university and didn't face any problem.

Thank you