Though the question is to Sai Kumar ji, I hope I can answer this.
Dear SourcingSpecialist,
When a company gives offer letter to the employee, it is an offer extended from employer's side. You have a right to accept or reject it.
Ideally your appointment letter should be given to you on the day of your joining or within a week. But there are firms who give you appointment letter only after 1 month of continuous tenure.
When appointment letter is given to an employee, he is given full information on notice period, other obligations for your perusal and you are supposed to sign the acceptance on its duplicate copy.
Once the appointment letter is signed and given, it means you accept the terms and conditions of the firm and hence are expected to abide by same.
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In your case, you were never given any appointment letter, neither have you signed the acceptance of it. So the question of notice period do not arise.
However, just resign on a good note by putting your papers down and submitting a formal resignation and give them atleast 2 days' time so that you can do handover.
See though formally you are not bound by the notice period clause, it never hurts to show a good image of yours, right.
All the best and hope it was of help :)