Unable to serve Complete Notice Period- personal issues employer denying experience letter

Hi seeking your advise as the current employer has 2 months notice mentioned in offer letter and I am only able to serve 20days notice + I have 10 Paid leaves in my account. They are not ready for buyout option for the remaining time and rest using to give me proper relieving. Following is the employment clause in offer letter Employment Status: Please understand that your employment, just like that of everyone at LRN, is voluntarily entered into. As a result, you are free to resign at any time, for any reason or for no reason by giving 2 months notice. Similarly, LRN is free to conclude its employment relationship with you at any time, with or salary in lieu of notice; and with or without cause. During the notice period, you will not be entitled to avail any kind of leave. This employment relationship cannot be modified at any time during your employment, except in a written agreement. As per practice, we will spend the first six months getting to know each other and evaluating whether this journey is right for both you and for LRN, after which time, contingent upon satisfactory performance, your employment with LRN will be confirmed.