Can employer give less notice "15 days and ask for 3months

Can you please help our appoitment letter says " Notice for Separation During the period of Employment, you can resign from the services of the Company by giving One month notice in writing or One month gross pay in lieu thereof .However, acceptance of your notice period by the company will depend on replacement being provided and handing over of the responsibilities & duties is done to our satisfaction. The Company however reserves its right to terminate your employment giving fifteen days notice or basic salary in lieu thereof. The Company reserves its right to recover amount of equivalent to one month gross salary on prorate basis, if you fail to give the Company’s required notice of your intention to terminate your employment. No notice of resignation will be effective if given during a period of leave of absence from the Company and during the notice period you will also not be entitled to avail any kind of leave. Further the Company may at its discretion relieve you from such a date as it may deem fit even prior to the expiry of the notice period in the event of you initiating the separation/submitting the resignation. Irrespective of the above, your resignation will be accepted only if you complete all the tasks already assigned to you. Relieving/Service letter would be issued to you only if you complete the exit formalities and handover full charge of work to your manager or any person designated by him including handover of all the documents, materials and any other information required to carry-out the work. Notwithstanding anything aforesaid, in the event that you execute a service agreement or other agreement(s) the terms of such agreement(s) shall always prevail. The Company shall have the right to recover such items from you or withhold dues, if any, to you from the Company. PLEASE confirm if we can challange the employee in court if he hasn't serve notice