can I get admission in IIIT BBSR if my jee main percentile is 91.52 & with state quota

HELLO SHUBANKAR
since it is very difficult to predict the exact rank but we do have a backup we have a formula to calculate the expected rank that is (100 – Total percentile) x 869010/100.
So according to formula your expected rank for present percentile for January session comes out to be 73692. Now the expected rank might change depending on the no of candidates appearing the april session. For ex if 12 lakh candidate appear the april session then just replace 869010 by 12 lakhs. But if you score above 85 percentile then you have a very decent chance of qualifying jee mains.
Now since the official cutoffs fro college are yet to be decided but let us analyse your chances by looking into the previous year cutoffs data
Since you did not mention your category let us assume it to be general by default
International Institute of Information Technology, Bhubaneswar
Computer Engineering    6140  -  19974

Computer Science and Engineering    7140  -  15315

Electrical and Electronics Engineering    17405 -   26006

Electronics and Telecommunication Engineering    21821 -   25497

Information Technology    6792 -   21292

After looking into the data it seems a little difficult for you to enter this institute

No worries since you have an april attempt left and most importantly baap of the exams i,e Advance which may directly lead you into IIts.

But if you are curious to know that which college you might land into with your percentile then you can use the college predictor link which has following features;

JEE Main 2020 College Predictor

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ALL THE BEST FOR APRIL AND ADVANCE!!