Hello suvarna

IIITs are of two types:

1. Indian Institute of Information Technology, and
2. International Institute of Information Technology

Indian Institutes of Information Technology are further of two types:

1. Fully funded by MHRD, Government of India. These IIITs are funded by Central Government and State Government in the ratio 50:50. This includes IIIT Allahabad, Gwalior, Kanchipuram and Jabalpur.
2. Not for profit Public Private Partnership (PPP). These IIITs are funded by Central Government, State Government and Industry Partners in the ratio 50:35:15. These in includes new IIITs like IIIT Srirangam, Kota, Lucknow, Sri City and many others newly opened IIITs.

International Institute of Information Technology includes IIIT Hyderabad, IIIT Bangalore, IIIT Bhuwaneshwar.

Admission to Indian Institute of Information Technology is based on common counselling conducted by JoSAA after the declaration of JEE Mains AIR.

Admission to International Institute of Information Technology is purely based on your marks in JEE Mains and the counselling is conducted separately.so go for counselling 

Good Luck. :)

Feel free to ask if you have any further queries.