Forcing to serve notice period instead of payout

Hello, So I put up my resignation from my company on 27th Aug 2022 and I requested my release to be of 26th September 2022, though I have worked till 6th October 2022 i.e almost 40 days. I am asking them to take the payout from my salary and also I have 20 days of Paid Leaves pending. But the HOD of my company is forcing me to serve 3 months notice period, which is not possible for me as my next organization has asked me to join by 17th October. I am willing to do the payout of the pending days but the company is not accepting the resignation only and asking me to give in writing that I will serve 3 months of the notice period. It would be great to get an understanding of what can be done. In the policy below statement is written: However, in certain exigencies, the employee may be relieved earlier on request with the approval of HOD by recovering the basic pay in lieu of a notice period from Full & Final Settlement. The concerned JMD & CEO/ Group President- HR, may at their sole discretion, relieve the employee before the completion of the notice period by paying a basic salary in lieu of the notice period. However, the company's decision in this regard will be final." Can I write a mail to the heads of the organization mentioning my last working day and just submit my system to the company and move to another organization? Can the company treat this as absconding even though I have asked for early release in exchange for the payout? Please help me out