Hello Rohit 

Any graduate can give Bank po examination whether you are completed your graduation with regular college or by open learning/ private. Degree obtained by private or regular has no role here .so give your best and grab the opportunity.

You can also read the detail educational eligibility criteria below

1. ELIGIBLITY CRITERIA:

(A) Essential Academic Qualifications: (as on 31.08.2019):

Graduation in any discipline from a recognised University or any equivalent qualification 

recognised as such by the Central Government. Those who are in the Final Year/

Semester of their Graduation may also apply provisionally subject to the condition that, if 

called for interview, they will have to produce proof of having passed the graduation 

examination on or before 31.08.2019. Candidates having Integrated Dual Degree (IDD) 

certificate should ensure that the date of passing the IDD is on or before 31.08.2019.

Hope this will helpful.