Non acceptance of shot notice period by employer

Hi I am from Bangalore. I work as an analyst @ Pvt Ltd company from past 2.5 yrs. Now I got a better opportunity in other company. where the joining date was after 30 days. In my current company notice period is 90 days. ( they also have a clause in offer letter- "company may elect to make a payment to you in lieu of part or all of the Notice period, as applicable") based on the above clause I taught I can serve 1 month notice & buy out rest 2 months notice. I discussed the same with my managers & HRD However, they gave a counteroffer, which I was not satisfied & denied. now they are telling they cannot relive my beyond 90 days. if I donot agree they will not be issuing any reliving letter also I did mention the clause of buy back. they are not ready for it. they tell that as per the clause we may elect only under certain circumstance. but we cant give you any buy back option for you & 90 days notice is mandatory. now I am in a dilama what to do next. Till today I have a good rapo in my work, I want to step out with a same good deed. but they are denying my request & not letting me out in a short notice. I request you to share some inputs how I can handle the situations