The subject acknowledges that due to certain issues, the Appointment Letter has not been issued. Thus, the initial responsibility for the derailment of duty falls on the employer. Typically, a formal letter of appointment is issued, and the employee is asked to fill in the details in the Duty Joining Report on their first day. Additionally, the employee completes a form to open a salary bank account at the same bank where the company holds its account. This process is usually followed to facilitate easy documentation and concurrent transfer of funds from the company to the employee.
Now, the problem lacks proper details. Why was the Letter of Appointment not issued and signed by the employee with the terms and conditions? As you mentioned, there are issues on both sides. You did not accept some conditions of the employee, and the employee did not accept some conditions of the employer. Consequently, nothing is binding. How can you credit the salary without any approval from the department where he worked?
If biometric attendance is in place, why has HR not checked the employee's attendance for the minimum number of days he was present on duty? Normally, I always review 25 days of attendance for the current month, plus the earlier months from the 26th day to the month-end (28/29/30/31, as applicable). That is, the calculation is from the 26th of the previous month to the 25th of the current month.
This applies to office employees, and field personnel are authorized by the managers. New joining employees are always shown separately, and their accounts are checked for probation, absence, sick leave, unauthorized absence, etc.
In this situation, you can either terminate or suspend, but the employer-employee relationship is not established. At most, you can check his attendance and what has been paid to him. If any excess has been paid due to the automatic credit of salary, you can seek a refund. A notice could be sent by the company with a show-cause notice for remaining absent during the probation period.