Can the employer terminate the employee without notice and pay compensation?

Dear Sir/ Ma'am,

Greetings!

I have a case where we have terminated an employee at 360 days, on an immediate basis.

We have not allowed him to serve a 30 day notice period, however, we have compensated the 30 days through an additional salary.

Please advise if we need to compensate the employee inclusive of the 30 days (notice period) in his leave salary and gratuity.

Or do we take the termination date as the basis of calculation for leave salary and gratuity?

Kindly advise.