Need Legal Suggestion For "Relieving From College Job".

Respected Sir & Madam Good Morning. I am Prof. Mohan RajKumar (Working as a Teaching Faculty in Private College, Chennai),I have 10 Years of Service in the Same Place. During My Initial Stage of Joining (Year 2012). They gave the Notice Period for (One Month only or One Month Pay), I have signed the agreement and joined during 2012. Recently Two Days Before (on October 09,2021), I received a Official Email from the Management Side, It Says All Employees Need to Sign the "New HR Policy" with Notice Period of (Two Months or Two Months Pay) if they wish to relieve. They told, New HR has joined in our office, so we are immediately changing the new HR Policy and New Rules & Procedures. My Point is They Have Sent Email About The "New Notice Period" Details in the Morning Time (around 8.30 am), and They asking us to sign and submit the document on same day itself (before evening). They are Sending Remainder Message on the Whole Day, to sign and submit the New Notice Period Document via Department Whatsapp Group and Phone Calls from Office. I have not signed in the new notice period document, I am not interested to abide their instant rule of notice period. Kindly Guide Me, How to Handle this Situation, I wish to Quit My Job in this month, Is its possible to follow the One month Notice, which is signed during joining or I need to serve for Two Months New Policy (That i haven't signed). Thanks & Regards Pro.Mohan RajKumar