Request for Guidance Regarding Resignation and Relieving Process

Dear Team, I am currently in a state of confusion regarding my resignation process and would appreciate your advice. On October 21, 2024, I submitted my resignation. However, to date, neither my last working day has been confirmed, nor have I received any response to my resignation email. I informed the management that I had received a very good opportunity in my preferred location and assured them that I would complete all major project tasks before leaving. I have since completed all major tasks assigned to me. I work in a team of five members, with two others focusing on the same front-end work as me. Despite completing the major tasks, the management has been making excuses and assigning me new tasks daily instead of discussing my release. As per the clause in my joining letter regarding termination, the terms state: You would be required to sign a twelve-month commitment as per the attached annexure. The company can terminate your services during probation by giving one week's notice for inadequate performance or indiscipline. A three-month notice period is required on either side or in the case of "Organization Name," payment of three months' salary in lieu of notice. Employees will pay the salary for the shortfall in the notice period, if any. I have offered to pay the salary in lieu of the notice period to facilitate my early release, but they are not accepting this option either. My joining date with the new organization is November 10, and I am uncertain about what steps to take next. Can I file a case against them? If so, how quickly would my case come into action? I kindly request your guidance on how to handle this situation effectively.