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You can apply for BA course in your mentioned college. It doesn't matter much when you completed your 12th. You can just apply for the BA course in the college when the admission starts. In some different colleges, there will be some age restrictions for some colleges. But you can also choose to take admission through correspondence courses in BA (i.e you don't need to attend the lectures but you can complete your degree by giving exams) .
You'll have to research a bit about the colleges that offer BA in Varanasi or so & apply for their course.