Can the employer force me to serve the notice period and can I file a case in my case?

Hi, I am actually working with an IT firm and had submitted my resignation on medical grounds stating that the climatic conditions are worsening my respiratory ailments and hence I have been medically recommended to leave the city and relocate. The company has a policy of 90 days notice period, my offer letter reads: "After completion of the Probation period, either Company or you may at any time terminate this letter of appointment without cause by giving in writing to the other party, 3 months notice. The Company reserves the right either to accept your pay and allowance / towards the notice period or demand for actual service during the notice period. You shall not be entitled to any notice pay if your employment is terminated in accordance with condition 7.6 of the Appendix 3 to this letter of appointment." Now I had filed for my resignation on 19th May and received a response from my manager on 21st May, who said he would have to consul his superiors and was insisting on my medical reports and certificates. I had shared my medical certificate with him but denied the medical reports as they are private and confidential. Post which I did not receive any updates and in the meanwhile they changed my last working date from 24th May to 17th August on the portal (without my consent), as the resignation was filed using a system generated portal. I called up the director and asked, he asked me to wait till 27th May as the process required the approval of the Senior Director, who is on a business visit in the US and in the meanwhile advised me to proceed on sick leave and in case of me having exhausted my leave balances, it would be treated as Leave without pay. Hence I went back and asked my manager, on the 28th May, about the proceeds on my case and he seemed to be very casual about it and said that they have not been able to talk to the senior director. So, I asked the director for an appointment to discuss the same on the 29th May, he questioned the credibility of my certificate and said that I had no choice but to wait until the senior director is back, which is another week and I told him about the medical condition, he said that I could stay home. Now, through my time in the company, I have been mentally harassed on multiple occasions and still feel that purposefully delaying a medical case is causing me a lot of stress and I also perceive it as harassment. I have secured another employment, which I haven't informed my current firm, in another city (keeping my condition in mind). Can I challenge this as a case of mental harassment and what would be the ideal steps that could be taken in this case so that I could be released soon? Hoping to seek a suitable advice in my case. Anticipating an early response. Best K.