I gave up my graduation in the 3rd year. How can I finish my BA graduation after 15 years of gap?

Nothing to do with earlier graduation. There's no option. Only do start from the beginning. If you are working many universities in every state offer graduation in distance mode. Again you have to spend minimum 3 years.

You will not be able to complete your graduation from where you left. But I would suggest pursuing B.A. From IGNOU as it is open university and gives weekend classes. It will be very easy to study and manage if you are already working. And it has same acceptance as regular B.A.