notice period (offer letter and appointment letter)

Hi There, I am Rahal currently working in cmm level 5 company and deployed in client location.I have received offer letter when I joined in that it is mentioned 2 month notice period .After 3 months I have received appointment letter stating with reference to offer letter we are providing this appointment letter and in that appointment letter it its mentioned notice period is 1 What is my actual notice period.Right now I have applied resignation and company is asking to serve 2 month notice period.Shall I go for buyout ie pay 1 month or 2 month basic pay as I have already got another job and need to join within 1 month.Can I send legal notice to my company as they are not accepting my resignation from past 15 days and saying will update tomorrow. Need your suggestion on this. Note:I have received scanned copy of appointment letter in gmail account .I have received hard copy of appointment letter in that hr manager signature is there but it is printed. Whether both of them is valid if I send legal notice .