Your management shown leaniency towards your request to release prior to completion of three month notice for which you were bound. Your manager approved your resignation but not the exemption for notice pay.
The general condition is that, to serve the notice period or pay notice period. The act of your managemnt is justified. You can ask the HR to provide you the details of account and deductions happened in the F&F. You are advised to check the appointment letter what exactly the terms put for notice period. Whether to count on basic pay or three moths pay. If it is basic, well you can raise your objection.