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.
Resignation can be of two types - (1) Prospective Resignation i.e., effective from a specified date in future and (2) in presenti 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 his discretion or convenience so as to relieve him earlier, it amounts to a counter-offer which will require the acceptance of the employee. If it is not accepted by the employee, the employer has to relieve him only by paying the notice salary to the employee concerned.
On the contrary, in the case of in presenti resignation, the employee needs immediate relief without complying with the notice clause. In such a situation he would be required to pay the notice salary or the employer may waive the notice condition. Same analogy applies to prospective resignation when the employer modifies the offer of the employee according to his convenience.
Therefore, Pallavi, your employer should pay you 3 months notice salary and relieve you.