Company Not Providing Relieving after Notice Period Served

Respected Sir/Madam, I am writing this letter to find out whether I can legally ask the employer to be relieved from my current role as I have a new opportunity. However I have already given notice period from 20 October to 15 November 2021 and if they feel that I have not given notice period with the company, then I am ready to pay or adjust the unused holidays. Let me take you through the detailed explanation, I officially resigned on 20 October 2021 after discussing over the phone with the manager. At that time he did not respond and I sent him an email. After sending resignation and completing one week of notice period, I got calls from leaders and discussion on retaining 26 October 2021, but it did not work for me and I refused to retain them on 28 October 2021 and Requested relief on 15 November. As per the terms of the appointment letter of 30 days. I was following them on acceptance but did not get any response. After I contacted HR, the manager has reverted for the notice period for extension which I cannot do. Considering notice period of my resignation from 28th October 2021 till 20th, is this correct? Also, they have not aligned anyone for the handover process. Seeing this, I have saved everything correctly in their portal and submitted the handover process notes of the work. But, they are not giving relief and insisting on extension of notice period and handover. Seeing my association with another company, I cannot continue with the Services and am prepared to give notice money if necessary in accordance with the Terms. What are they doing right? If I am submitting proper data and process notes of the work. Do I need to stay and give more handover?