Offer letter and appointment letter are two different things.
You may show the offer letter, appointment letter, leave policy, HR policy, Service Rules and Regulations, Conduct and Discipline Rules, Exit Policy that are mentioned in the appointment letter to an able Labor Law Consultant/Service Matters Lawyer/Law Firm.
The enactments that apply to establishment/employer/employee shall prevail upon any private agreement/rule/policy that employer has drafted and signed with employee.
Your counsel that has examined all docs on record can opine whether 90 days notice period is indeed applicable to you or not........................and also on equitable option of notice pay in lieu of notice period!
You may spend qulaity time with your counsel.