Dear Arun C. Kumar,
You've already received lots of inputs, however let me add to it just a bit.
From your post I interpret that your Company is purposely bringing in the 'confirmation' issues to get you to extend your notice pay, they cannot force you to serve 3 months notice since your were not 'confirmed' at the time of your resignation.
If your company tries to play tricks with you and refuse to relieve you or issue relieving letter then please escalate the matter internally.
(The following may not be relevant to you, however I would like to share this perspective)
In my experience, I have seen some Sr. folks in operations playing such tricks with employees. Sometimes, they do not have logic in their argument hence they behave badly with the employee and provoke him lose his cool and say/do something unprofessional, and then they complain to HR about his behaviour and try to get the employee terminated. Their basic objective is to pass a message to other employees that if they don't follow instructions of Sr. Ops guys then the employee's relieving will be screwed. You must remain calm and not get provoked.
I'm sure someone in top management will see the merit of your case and help you with your relieving.
If you are sure that no one in your Company can/will help or issue clean relieving letter, then don't waste your time behind them, try to build a convincing case to your prospective employer so they allow you to join without relieving letter.
Not sure how much this will help you, but i'm just trying to give to you a different perspective/option.
Regards,
Ritesh Shah