Though the question is directed to Sai Kumar ji, I hope I can answer this.
Dear Sourcing Specialist,
When a company provides an offer letter to an employee, it is an offer extended from the employer's side. You have the right to accept or reject it.
Appointment Letter and Notice Period
Ideally, your appointment letter should be given to you on the day of your joining or within a week. Some firms, however, issue the appointment letter only after one month of continuous tenure.
When an appointment letter is issued to an employee, full information regarding the notice period and other obligations is provided for your review, and you are expected to sign the acceptance on its duplicate copy.
Once the appointment letter is signed and issued, it signifies that you accept the terms and conditions of the firm and are expected to adhere to them.
In your situation, you were never provided with an appointment letter, nor did you sign the acceptance of it. Therefore, the question of a notice period does not arise.
However, resign on a good note by submitting a formal resignation letter and provide them with at least two days' notice so you can facilitate a smooth handover.
While you are not formally bound by the notice period clause, presenting yourself professionally can leave a positive impression.
All the best, and I hope this was helpful :)