Hi Deepika,
From another of your posts today, regarding pay slip formats what I understand is that your firm is an IT company of about 23 employees for which only the PT is deducted from the salary and the rest paid to the employee. It is not clear on whether there is a TDS deduction as a non-employee or whether there are PF or ESI deductions for employees.
The relevance of the above information here is due to the question on whether your company has all correct documentation or legal processes in place.
The current post more than performance issues of the employee seems to focus more on attitude or employee-employer perception conflicts. If there is a performance issue, then there should be records of discussions and performance improvement plan initiations, before the member's services are terminated.
Judging by the member's attitude it looks like he my not quietly leave. So it is better to either pay the notice period amount as well or to have a proper performance assessment process along with warning letters for misconduct if any, so that in further instances, the member cannot claim that he hadn't been warned or intimated.