You may go thru Shops and Commercial Establishments Act of your state which should be available at the website of Dept. of Labor of your state or you can download from internet or buy from market, and go thru clauses on, issuance of appointment letter, Notice of dismissal, Hours of work etc……………………………………………………and relate it with your length of service and find out what is the notice period stated in it for your length of service.
e.g. it might be stated in clause on “ Notice of dismissal” that after 3 months of service notice period to be given by employer shall be 1 month.
If it stated so then even if appointment letter is not issued you may succeed to claim such notice period and notice pay.
If there is a clause on issuance of appointment letter and appointment letter I not issued by employer then it is violation by employer and Inspector under this Act ( it might be Labor Inspector holding this charge too) can penalize the employer.
If Inspector takes n action then even if employer issues Appointment letter you may either decline to take it or you must receive it in current date only on which it is supplied to you and you shall have the right to reject the clauses in appointment letter that are not acceptable to you.
You may not accept the appointment letter on the spot and take it home and consult your counsel.
Another view point is that even if appointment letter is issued to you and notice period during probation period is stated as NIL you may refer to the Shops and Commercial Establishments Act of your state and claim notice pay.
Notice period during probation period can be NIL.
Even if a probationer is to be terminated company should follow Natural Justice.
You may consult elders, trade union leaders, lawyer for better understanding of the posts in this thread and do not proceed on your own.