Is it mandatory that I should submit a resignation and serve a notice period - have not received a posting order/appointment letter?

Hi, I was not given an appointment letter/posting order of any sort at the time of joining on probation, or even upon confirmation as a staff. I am working in this institution for last 2.5 yrs. Is it mandatory that I should submit a resignation and serve a notice period since I have not received a posting order/appointment letter of any sort.

Dear Harikumar,
Technically, if the appointment letter is not issued then the employer-employee relationship is not established. Since there is no contract between employer and employee, a question of terms and conditions of separation from the company do not arise.
In view of this, should you abandon employment at your will? The theoretical answer could be 'yes' but there are practical things that one needs to look at.
If you abandon employment, then the employer is not liable to give you the "Service-cum-experience Certificate". If you do not acquire this certificate, then how you will show you tenure at this company?
Whether the appointment letter is issued or not, your current employment was a source of livelihood for you. Therefore, it is appropriate for you to leave the company on a good note. Our future is unpredictable. Our life is nonlinear. Who knows the situation may force you to come back to the current company. Therefore, prudence demands to keep the door ajar. In case if you abandon the employment, then the door of that company will close for you permanently.
Thanks,
Dinesh Divekar

Dear Dinesh,
Thank you so much for the prompt reply.
During my tenure I have collected 3 "still working certificate", one every 6 months. Does this document do any good, in case the HR does not provide me an Experience cum service certificate? Am I liable to pay the notice period amount, in case of one day resignation?

Hi Hari Kumar,
What you have in hand may not be sufficient. It would be prudent to complete the notice period as required and get your detailed experience cum service certificate indicating your DOJ, DOR , salary received, nature of work etc. Was wondering how you have worked for 2.5 years without any proper employment order in place.
Always please ensure to have some proper employment order/ proof for salary in place which will be useful for your employment applications / Bank loans.