Resignation Period

My resignation period is for 60 days. I have informed management that I will only be able to serve it for 30 days and I’m ready to buy out remaining 30 days or i have asked them to apply my leaves for rest 30 days (that i will not he able to serve). I have everything in written, about my intent of serving only 30 days. In my employment letter its written that i have to serve 60 days and as well as its written that ‘Company reserves the right to pay or recover salary in lieu of notice period.’ I have emailed my manager to allow me options because its written in my employment letter. The reason i cannot serve is because i have another job and they are only allowing 30 days of wait time, additionally they( my new employer) are ready to buy out my notice. My organisation is acting adamant and i will not be able to serve. I’m aware that my organisation will send me settlement notice after i leave. My question is, can i pay the remaining 30 days and request my relieving letter and experience letter.