You have been working for 1.5 years and are still waiting for your appointment letter. Kindly let us know if you have received any job offer (before joining the company) or not. If yes, you must have returned a signed copy to them as well. How did you submit the signed offer letter, through email communication or hard copy? Also, please mention the mode of salary payment, is it through a bank account or in cash? Are salary slips being provided? This information will help us provide a more accurate response.
As of now, if you have returned a signed offer letter to the company via email, and you are receiving your salary through a bank account along with salary slips, you need not worry much. However, you should request your employer/HR Manager/any other relevant authority to issue you an appointment letter, emphasizing its importance such as the notice period clause or non-disclosure clause. Hopefully, the management will understand your concerns and issue you an appointment letter retroactively.
Regards,
Prabhat