Dear Pallavi, what I understand from your post is that when you are prepared to serve the entire three months' notice period from the date of submission of your resignation, the management intends to relieve you in 15 days.
Types of Resignation
Resignation can be of two types - (1) Prospective Resignation, i.e., effective from a specified date in the future, and (2) In Presente Resignation, i.e., effective immediately. When there is a period of notice specified in the contract of employment, prospective resignation effective from a future date that includes the entire period of notice, if so submitted, is an offer by the employee to comply with the notice condition. If the employer modifies it according to their discretion or convenience to relieve the employee earlier, it amounts to a counter-offer that will require the acceptance of the employee. If it is not accepted by the employee, the employer has to relieve them only by paying the notice salary to the employee concerned.
On the contrary, in the case of In Presente resignation, the employee needs immediate relief without complying with the notice clause. In such a situation, they would be required to pay the notice salary, or the employer may waive the notice condition. The same analogy applies to prospective resignation when the employer modifies the offer of the employee according to their convenience.
Therefore, Pallavi, your employer should pay you 3 months' notice salary and relieve you.