Hello dear, after studying the cutoff of previous years I can say, in this rank, you can get AIIMS Patna, Rishikesh and Raipur and the maximum probability is of AIIMS Patna. Additionally, I have attached a link where you will find previous years cutoffs, do check it for getting a more wider view.

https://medicine.careers360.com/articles/aiims-mbbs-cut-off

And ranking which one is best is bit tough, but still, I have provided a list and it is based on personal views of experts so you can trust it moreover you are free to do your research.

1. AIIMS Delhi
2. AIIMS Jodhpur
3. AIIMS Bhubaneshwar
4. AIIMS Patna
5. AIIMS Rishikesh
6. AIIMS Raipur
7. AIIMS Bhopal

Hey. Here is a list of all the AIIMS Institutes and their respective cut offs for the previous year. You would require a rank around this range for a fair chance of admission here.

All India Institute of Medical Sciences, New Delhi 53

All India Institute of Medical Sciences, Bhopal  647

All India Institute of Medical Sciences, Bhubaneswar 542

All India Institute of Medical Sciences, Jodhpur 459

All India Institute of Medical Sciences, Patna 1222

All India Institute of Medical Sciences, Raipur 1,145

All India Institute of Medical Sciences, Rishikesh 769

All India Institute of Medical Sciences, Nagpur 1324

Considering this you might have a few chances though they seem to be a little less.

Best of luck!