Hello ,

First of all I would like to tell you there are three kinds of IIITs in India :-

1. Indian Institute of Information Technology , Government like IIITM Gwalior etc.
2. Indian Institute of Information Technology , Public Private Partnership. like IIIT Pune  etc
3. International Institute of Information Technology , Private like IIIT Hyderabad , IIIT Bangalore etc.

Now talking about above 1-2 cateogry colleges take admission through JOSSA Counseling for which you can apply after commencement of JEE Mains and JEE Advance and admission is given on the basis of JEE Mains rank . The 3rd cateogry also participate in JOSSA except IIIT Hyderabad . IIIT Hyderabad has a separate counseling portal through JEE Mains and JEE Advance rank basis admission for which you can check its official website . Also IIIT Hyderabad conducts a separate test for its entrance .

And one more thing I would like to add JOSSA Counseling is not started yet it will be started after JEE Advance results .

Hope this will help .