A. Once the employee joined with particular designation for the company that have bounden duty to issue Appointment Order at the time of joining. There must be a terms and conditions and formal deciple code for the employee alongwith notice period towards the resignation.
B. In your case, no appointment order issued by the company. However, have you received any offer letter? was there any terms and conditions? Have you received company policy through mail? If yes, what is there in the policy? don't worry, employer cannot insist to serve 3 month notice in the absence of contract. Moreover, they don't have right to hold your PF and relieving letter. You send a mail by narrating all the facts pertaining to non issue of appointment order and mention your last working day. If you get any trouble from them, issue a legal notice to the Reporting Manager, HR and Director of the Company.