Notice Period Buyout

I resigned from my current company 10 days ago to join some other firm. As per the requirements of the firm that I’m joining, I can serve a notice period of not more than 30 days but my employer/Manager is unwilling to allow me to serve a short notice period even when I'm offering to buy out my notice period. Providing some context for a better understanding of the situation: 1. I accepted the terms of my offer letter at the time of joining, in which it is stated that "The Company or employee may, at any time during the course of the employment terminate the employment by giving 60 days-notice or salary payment in lieu of that notice, by stating their intention to do so in writing. For the purpose of this Clause, salary shall mean the most current base pay. Such shall apply following your probationary period." 2. However, after working for 7 months, I received the appointment letter which apparently got delayed due to some technical issues. I was given a day's time to accept the terms and share a signed copy. But I never actually did it. Recently, when I reviewed it, I noticed they made a change to the termination clause. This is the clause as per the appointment letter "Termination of your employment by you or the Company at any time during the employment, under normal circumstances, shall be based on a (60) sixty days’ prior written notice, or, payment of salary in lieu of such notice period or payment of proportionate salary in the event of any shortfall in the said notice period, as per the then applicable policies of the Company in this regard. The Company may at its sole discretion waive all or part of the notice or allow you to pay salary in lieu of the notice period required to be served by you in the event of your resignation. Your resignation would have to be accepted by the Company to become effective. Once accepted, the resignation cannot be withdrawn by you without the express consent of the Company". 3. This is the current policy of the company: "Effective February 1, 2015, employees are required to serve 60 calendar days’ notice, (hereinafter referred to as the notice period), in case one wishes to resign from the services of the Company. The Company does not provide any option to buy out the notice period. The Company would under normal circumstances not agree for an early relieving. However, if the employee request for an early relieving, the same shall be granted at the sole discretion of the management. To this extent, this policy will supersede the terms of employment signed by employees. Employees intending to resign shall address the resignation to Reporting Manager with a copy to the HR Manager." Since I never signed the appointment letter, am I still required to abide by this clause/the company policy? If not, then will I still be eligible to receive the relieving/experience letter from the company if I offer to pay the company in lieu of the notice period even without my manager’s consent?