Quick answer: No
Most banks ask for a minimum qualification of graduation – like B.A., B.Com, B.Sc, BBA, B.E., etc.
If you only have a Diploma, you will not be eligible for most bank jobs.
However, if you have done a regular graduation after your diploma (for example, a B.E. or B.Tech), then you can apply.
So, if banking is your goal, your next step should be to complete your graduation.