Did you submit your resignation letter complying with all the prescribed formalities, like advance period notice etc? What were you told by your Branch Manager or department head at that time and afterwards? When was the last working day you attended at the ban? Was there any usual farewell meeting and formal handing over of relieving letter? Did you get any benefits like Provident Fund salary arrears etc?
Usually PSU banks do such things very systematically as there are established system of many decades. Not just that; the colleagues themselves will be ensuring all these.
I guess that there is some communication gap or strained relationship with you and the bank where you were working.
It is quite a long period from the time you resigned. You should have taken due course of action.
I am just not able to digest your problem. Such things never happen in normal situations in banks.
There can be some delay of actual handing over of relieving letter if there is some unexpected situation arising. Even then, being an ex-employee you would have easy access to your former colleagues. They would have helped you.
I am assuming that you had submitted resignation complying all prescribed formalities , and stopped attending office only after the last day of the prescribed notice period and you were never informed of any problem in accepting your resignation, you were not on any bond or contractual obligation.
If that is right then:
1. Visit the office where you worked last and submitted resignation. If everything was right the relieving letter or copy will be available in your (employee file). Or at least they will be able to help you.
2. You may contact the employees' union representative at that office or at leaders at the regional or head office.
Now, regarding the CGL matter,
If you had not mentioned about your bank job, they will not ask for any relieving letter.
However if the facts are different than what I assumed, and you are not relieved by the bank for some valid reasons like some disciplinary proceedings, some outstanding liabilities etc, then things may turn bad for you if the bank proceeds with some court case, publishes notice in newspapers, finds about your new job and informs that employer etc.
So take genuine efforts to get the relieving letter at the earliest.