Greetings aspirant!

Surely, you can sit for Bank exams, both for government as well as private. Though eligibility criteria can vary from exams to exams. Minimum requirement usually is :- age between 20-30, and bachelors degree from a recognised institution. There are basically two post one of clerical and other of PO.

Here are some links to help you further. https://competition.careers360.com/articles/ibps-clerk

Hope it helps.
Thankyou!

As you have completed your graduation, you can appear for competitive examination of various banks for government as well as private ones. For government examinations such as SBI Po, IBPS Po, RBI Grade B Officer, RBI assistant egc. The basic criteria is that the candidate must has completed graduation in any discipline from a university which is recognised by Central Government. General category students of 21 to 30 years old, are eligible to appear for SBI Po for 4 times. For IBPS Po, the minimum age limit is 20 years and maximum 30 years where there is relaxation for reserved category students. For IBPS Po, you must have secured at least 60% marks in Graduation.

You can check the eligibility criteria here http://competition.careers360.com/articles/sbi-po