Notice period buyout and no dues

Hello All, I had an official notice period of 60 days and I gave resignation to my previous employer upon getting a good opportunity. When I got selected in the interview process, my new employer said that if there's an option for notice period buyout/buyback, we will do that you just ask your previous employer. I gave resignation after getting offer letter, and 2 days later I submitted all the belongings. At the time of submission, I had a very long conversation with the management and HR about leaving the company in that short notice and also for the notice period buyout. Now my offer letter does not mention that I have to pay notice period amount when I will not be able to server notice period. The line that is mentioned in my appointment letter is "In case you wish to terminate your job, you need to serve notice of two months duration" and nothing other than this, but still when I was having conversation they asked for 2 months of salary. I said that this is not mentioned in my appointment letter but they are saying that this is not mentioned there but it is in our policy and we don't mention it because we believe in our employees that they will not do anything. I told my current employer that this is what they are saying, so they said that if you'll not pay then they won't share the relieving letter and experience letter. So I paid 2 months of salary as a notice period compensation. Now I want to claim the buyout amount from current employer, they asked me to get no dues from your previous company and also tell them to mention that you have paid for notice period buyout but my previous organization denying to give it in written that they took 2 months of salary. Now for my backup I have an email where they are indirectly asking for 2 months of notice period compensation and I have recording of the conversation we had when I have submitted the company belongings where they have asked for 2 months of notice period and agreed upon they have not mentioned it in appointment letter. I got a letter of no dues, without mentioning the notice period buyout option in that no dues and want me to sign on it and give it back. Please suggest me what to do now, should I wait a little more and give them time to finally give me a correct no dues with notice period buyout point in it or should I file a case to labour law department?