Dear Aspirant 

If you are an Indian and belonging to any of the state in India, then you don't require nationality certificate. If you are taking admissions to other than your home state then you need have domicile certificate otherwise you don't need if you are talking admission in your home state. 

For NRI ie non resident Indian and foreign student there may be requirement of such certificate. 

Good luck for your counselling procedure!

Feel free to ask if you have any further queries.