Relieving after serving notice period

I resigned from an IT services company on 20 April 2022 due to better opportunity and dis-satisfaction. As per the appointment letter, an employee has to give 3 months notice before leaving the company.  At the time of resignation I did not have any project/work. After serving 45 days of serving notice,  the manager has assigned a new task and asked me to complete it before last working day (19th July 2022). otherwise he do not want to issue relieving letter.   Completion of this new task before last working day may not be possible even i work 12 hours/day. The date of joining in the other compay  will be on 21 July 2022. If not joined on this date, the offer will be cancelled. They may extend only a few days on request. My anxiety now is that if the current company will not relieve me and issue relieving letter before 19th July 2022, I  will become jobless. Because I lose current job due to resignation and other job offer will be cancelled automatically. Please suggest whether i could file the case in court if current employer will not issue relieving letter on last working day (19 July 2022).