According to their official site->

Https://aaa.iiita.ac.in/

1. Admission : The Institute allows admission in all UG & dual degree program through CSAB & DASA, All M.Tech. and Integrated M.Tech. Ph.D. program through CCMT, MBA & Ph.D. Through Institute level Examination. After getting the admission through aforementioned process the students should report to this cell for completing other formalities, then Cell issuing registration number and keep record of all the admitted students..But for b.tech seat , the only way is JEE MAINS.

Please check their site for more information.

Hey Aspirant 

Candidates seeking admissions to B.Tech shall be admitted on the basis ofJEE Mainor GUJCET ranks through counselling conducted byJoSAA(national level) and ACPC, Gujarat (state level), respectively.
Application to both M.Tech and Ph.D. course shall be invited in online mode only onIITRAM, Ahmedabadwebsite.
To be eligible candidates must have passed 10+2 in science stream with Chemistry, Physics, and Mathematics as compulsory subjects.
Candidates must secure minimum 75% marks or be in the top 20 percentile in the class 12th examination conducted by the respective Boards.
For admissions to M.Tech candidates shall be admitted on the basis ofGATEscores and/or entrance exam conducted by IITRAM.
Minimum of 55% marks in B.E. /B.Tech. or equivalent in a relevant specialization (50% marks for reserved category candidates).
Admissions to Ph.D are offered on the basis of performance in written test followed by an interview.
Candidates need a Masters Degree in Engineering or Technology/Sciences/Humanities/ Management or equivalent degree, with minimum 60% marks (55% marks for SC/ST) for admission to the concerned specialization in Ph.D.
The reservation criterion is as per the norms of Government of Gujarat.
Hope it helps

Yes, IIIT's are institutions governed by central government of India. And this college allows admission only through jee mains ranking like NIT's. You will need to take part in counselling like JoSAA and CSAB to get aseat in this college. There is no other way of securing a seat in any of IIIT'S.