My company not relieving me in 60 days instead of 90 days even after i offered to adjust leaves

Currently I am working in Mumbai from August 2019 till now and i have resigned from my current position on 10th November 2020. Now as per mutually agreed terms, I need to serve 90 days of notice however, I have expressed to my reporting person that i intend to leave within 55 days (last date to be 3rd Jan 2022 instead of 9th February 2022) as I want to spend some time with family by going for vacation for few days and later on join future employer in the middle week of January 2022.I mentioned that i have ~50 days of leaves which could be adjusted so that i could be relieved accordingly. Now after having multiple face to face discussions initially and numerous email sent to reporting person and head of HR, he stopped responding over email. And HR is constantly saying that it needs reporting manager's approval to execute exit formalities for 60 days. Additionally, i have made sure that my current team mates are trained and can perform all tasks assigned to me and have started to send reports to concerned people. For everyone reference, i am sharing the employment contract terms "During or at the end of probation period of services can be terminated by giving three month's notice by either side, in writing or three month's salary in lieu of such notice. However, the company may , at its sole discretion relieve you of your duties any time during the notice period, and in that event, you will be paid salary upto the last working day only." Now i am in a fix how i should handle above situation??