Fired From IT Company

I was fired from an IT company in gurgaon after being in 2 months in pip.During exit I asked them to extend my pip or to let me serve the complete notice period of 3 months since I did not have a job.They did not listen and relieved me on the same day.When I came out I had to face so many difficulties finding a job because every recruiter asked as to why I left my job when I had no offer from another company.This also had huge impact on my health and I suffered from severe depression and still taking antidepressants.Do I have a scope for filing a case against this company for rushing through my exit and not giving me time to look for a job?