Notice Period

Good Morning, My name is Raju Goswami, I have given resign from my job as I am getting a good opportunity, My company is asking me for the notice period of 3 months or to pay the recovery amount of 2 CTC if I want to leave early in one month. I was discussed earlier also but not in writing. Now in my Appointment letter, it is clearly said that if I want to leave the service.. I would have to stay for one month notice period, or give one CTC if I want to leave without one month notice period. In my new company where I am going to join on May 1st, I have managed and convinced them for 45 days.. Which will completed on 30th April'22, My current company has accepted my resignation and asked me to stay for 3 months which will be completed on June 16th. As I have resigned on 17th March 2022, I want to leave on or before 30th of April (45 Days) with my relieving letter, Experience Letter and No due certificate without any clash with my current company if possible, but at the same time i dont want to bear any unfair with my self too. If I have to fight for this I am ready. So please explain me how will it possible for me to approach them ( HR team) in legal, I mean I want to request them but the impact of ny mail drafting should be like I they can not do anything wrong with me. Again reminding you that in my appointment letter it's clearly mentioned that only one month I have to serve a notice period, Please explain me in details with Sections ( My rights, what company could do with me if they want, how can I fight for my rights etc.. )