To work in a Public Sector Bank, you need to appear for IBPS PO exams. For that you can be a Graduate in any discipline. But to work in a Private Banking sector, as you are already studying B.Com, you can complete your MBA in Banking and Finance. That will help you with opportunities in Private Banks. You can also study M.Com (//M.Com) in Banking and Finance,  M.Voc in Banking, Stocks and Investment, PGDM in Banking Management, etc. So we would suggest you to complete B.Com (//B.Com) and take up any of these courses based on your interest.