which Notice period is valid among next - of appointment letter OR said in changed policy?

The notice period for employees for submitting resignation is 90 days in general, to help the employer for finding suitable alternates.  The laid down policy, circulars issued from time to time holds good as personal communication, and the appointment order need not contain all such rules and regulations on leave, notice, disciplinary proceeding also, as a common agreement is that employee follows all rules and regulations in force.

Either surrender the leave or pay the 3 months salary or contact a local advocate to challenge such breach of the condition if all your efforts to convince HR fails.

Terms and conditions of your appointment / service contract shall govern the issue.

Amended policy shall be applicable prospectively and not retrospectively, if any, 

You can very well go by the T & C of the employment offer letter. 

The company may change its policy or regulations at a later stage, if you have not given consent for this you had a choice of quitting the company for willing to abide by the change in company's rules or regulations.

If the company did not bother to obtain any such consent from you earlier and is no insisting you to serve  the extended notice period, it can be considered as an illegal demand and can be challenged in court of law provided you have so much time.

Hence you can decide about it by taking a wise decision at right time to protect your interests.