Clarification on Notice Period and Standing Orders
Your question is not clear. In general, the rule to be followed is standing orders or contract, whichever is more beneficial to the employee. Since you do not have certified standing orders, model standing orders will apply. Therefore, if the standing orders require more than 3 months' notice, then it will apply. If not, the 3 months specified in the contract (appointment letter) will apply.
You cannot take shelter under the ID Act to dismiss someone for a lesser period. Unless, of course, there was misconduct, and the termination is based on the recommendation of a domestic inquiry and justified by the gravity of the misconduct.