Hi Samaya
I would like to highlight that probation period means that the employer can terminate the employee at any time without any prior notice period. And thus the same applies to the employee. If you feel like leaving the company during your probation period, you are not liable to serve any notice period for it.
I feel your company is simply exaggerating the issue probably because you have some unfinished business there. I will recommend that you speak to the concerned HR/supervisor for what they exactly want from you, because legally you are not bound to them. They might be thinking of recruiting a new person and getting him/her trained by you so that no burden of training comes on their heads. So try out a polite talk on this issue.
And lastly, since you have not received any appointment letter, the company won't be issuing you any relieving letter either. Next time keep in mind the importance of getting an appointment letter and simply move on form here. All the luck!
Anshu