Regarding exit during probation period

Hello All, I am working with Delhi based company however I am deployed with one of their client in Gurgaon, During joining my payroll company provided me appointment letter with below details "Probation: Initially the appointment shall be for a probationary period of 3 months. Thereafter, if your services are found satisfactory, you shall be issued a letter of confirmation. Your probationary period can also be extended at the discretion of the company.During the probation period either the company can terminate the appointment or you by giving 15 days notice Termination: a:) On confirmation of your services you may terminate this appointment by giving 90 days notice in writing. No adjustment to be made in lieu of notice period at the time of exit." As of now they have not given me any confirmation letter that I am now their confirmed resource neither any letter that my probation period has been extended. I am having some personal issues and will not be able to work longer in Gurrgaon and wanted to quit the organisation. I have put down my resignation and asked for early release, Now they are forcing me to serve 90 days. Though I have not received or signed any confirmation letter that say I am bound to serve 90 days notice period. I tried for all negotiation already served 30 days notice period hoping for smooth exit but they are not agree to provide me any early date. Please let me know any solutions. Regards, Ravi Singh