Notice period is 60 days - if I can take legal action against the company based on the appointment letter clause?

My Notice period is 60 days, as mentioned in the Appointment letter, but the company is giving me 27 days only and put my LWD 31-DEC.
I have discussed this with HR, but they say the project is over, and the client shared the project closure, so your LWD is 31, and you are not paying for the remaining 30 days.

The clause below is mentioned in the appointment letter, but the company is still breaching the clause. So, I want to know if I can take legal action against the company based on the appointment letter clause.

Company clause:- company name removed

The contract of employment is terminable by either party by giving 60 days' notice in writing; however, the contract agreement between (company name )and its customer supersedes the notice period defined by (X COMPANY ) for its employees till deployment. Either party is not bound to give any reason thereof. The (X COMPANY) reserves the right to pay or recover salary instead of the notice period or to relieve you before the expiry of the notice period.
All payments and recoveries made under this clause will be based on the Basic salary.
In the event of any breach in the terms and conditions stated in the Services Conditions and/ or Non-Disclosure Agreement or any cause of misconduct, your services are liable to be terminated without any notice or payment in lieu.

Please guide.

Your notice period clause is not clear. Which is company X? There is a mention that the contract between the company and its customers will supersede the notice period....till deployment. What does it mean? Similarly, either party is not bound to give any reason thereof, of what? Is it that the contract between the customer and the company will decide the contract between the employee and the company? That is, the employment is a fixed term contract and the same will come to an end as soon as the customer decides to discontinue the contract with the company. There can be fixed term contract but there should be a mention about the date of termination of contract, say, one year/ two years/ three years from joining OR completion of a particular project/ task. Then the employee will have an idea as to when his employment will come to an end, say on a particular date or he can prepare himself to get some other employment when he has an idea about the completion of the project. But in this case, it is not a project or time which governs the contract but it is the customer who decides. As such, the contract is not maintainable under the Labour law. Again, there is another mention that the company has the right to pay notice pay. That means, it is a managerial prerogative either to pay notice pay or reject it. This is also one sided and will not be maintainable.