You CANNOT apply for Bank jobs till you become a graduate degree holder from a recognised University.
Exams are held by IBPS according to the vacancies in the banks in the government sector. PO and Clerks and Specialist Officers Exams are conducted by IBPS.
I therefore recommend you to become a graduate first and score minimum 60% to be on the safer side. You can do graduation with any course of your interest(it would be better if you do graduation in commerce subjects)
Hope this helps you.
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