I would appreciate real honest replies to this:
1. How long was your employment tenure with the company?
2. Was there any act of misconduct or any misbehavior done by you?
3. How were your relations with your reporting manager?
4. What is the reason for your absconding?
If you can't answer here, ask yourself and get the answers to it. The reason why it's necessary to know the answers to this is because, by absconding, you have chosen the wrong path. Now, to get your experience letter, you ought to make up for this. First of all, going absconding and then asking for your experience letter after 3 long years itself raises a question on your professionalism.
However, better late than never, you need to realize and accept all your mistakes. Going to court will only worsen the situation. There are things that could be done in a better way. Visit the office with all your documents, i.e., your appointment letter, payslips, confirmation letter, increment letter if any. Speak to the HR, speak to your reporting heads or managers (if they are still working there), apologize for what you had done. If required, submit a written apology letter and an application for your experience letter.
For sure, this will not be sorted out so soon and easily. You will have to build a good relationship with those in the office, making them understand that you are aware of what wrong you would have done and have taken measures to improvise on the same. You will have to do continuous follow-ups but without getting frustrated, in a nice cheerful manner.
But in all this, the first thing you need to keep your temperament cool and do not behave aggressively. Again, to remind you, many issues can be resolved by discussing it over with a cool head and warm words. Make sure you do not speak in any irrational manner. And kindly behave as a real professional now.
Each time that you meet the HR, after you leave the office, drop a mail about the discussion you'll have. Then at least you'll have some written evidence.