There is no appointment letter given to you/accepted by you,hence there are no agreed agreed terms of contract of employment.hence no conditions of notice for seperation.
Were you issued any offer letter before your appointment.
Is the company issuing you any salary slip.
If nothing is given , the company can be acused of grave violation of the laws, and can be penalised.
This seems to be a fairly large retail house ,as it has IT department,HR.
It shall be appropriate to see a lawyer/experience person,with all the documents you can collect about your job in the company,who shall guide you on course of action.
The action of HR guy in indivisual capacity,and as employee is not just. This HR guy knows the company has not issued any appointment letter and still forcing you to write notice of resignation, giving 2 months notice period, and if you don't serve , you tender notice pay.
Just remind this HR person, there is no notice period.
It shall be appropriate that you submit in writing that you were selected by the company on dated..........and despite your representations dated......,and dated........you have not been provided with any offer letter and therafter despite your representations dated .,and dated......no appointment letter was provided to you.
There is no agreed terms of appointment and resignation, and you are tendering your resignation with immediate effect.In this matter you have already represented to HR person (name and designation office address ) on dated.and dated .... . Demand to settle your account,issue you work experience certificate,F&F,form 16,relieving letter,PF accumulation report,PF withdrawl/transfer forms etc.
If any backdated appointment letter is handed over to you, you may sign your acceptance (only if acceptable to you, after showing it to your family, well wishers and a lawyer) in the current date.
Don't accede to their unfair demands.
Be polite, cool,composed and firm.
Be smart and maintain your rapport.HR person under compulsions of his/her job, is pressurising you.
Collect all records to prove your experience with the company.