What happens if I don’t serve my notice period in full

Dear Sir / Ma’am, I have sent resignation to my present employer on 6 Apr 2021 asking to relieve on 15 May 2021. But they are stubborn to relieve me on 6 July 2021 only. The problem is if I don’t leave them my 31 May 2021 I’ll lose my employment with the future Organization. I am worried if I leave forcefully they might act funny and not give my relieving letters and full and final settlement. Kindly suggest me in this regards. As per my Letter of Appointment: it is mentioned as “Notice period will be three months either side in case of discontinuation of services. Minimum of 60 days working notice shall be must and relieving from service will be discretion of Management. If any previlege leave is due to you at the time of termination under this clause, you will be paid proportionate basic salary in lieu of such leave. It is to be noted that it is neither mandatory nor binding upon the company to adjust accumulated EL against the three months notice period stipulated above in the event of a request from you to that effect and the same shall be at the total discretion of the company” However in the subsequent salary revision letters they have mentioned the below statement “Notice period will be 3 months either side in case of discontinuation of services. All other terms and condition of your employment remains unchanged” I have been serving this Organization from 29 Jul 2016. Kindly advice how should I go about this situation.