IIT

If your category rank (OBC Rank) is 3032, then the IITs available to you are:-
1] IIT Dhanbad - Geophysics (5 Y)
2] IIT BHU - Bio (5 Y)
3] IIT Kharagpur - Applied Geology (5 Y)
Unless you need the IIT Tag to flaunt in front of your relatives and unless you have some specific interest in these fields or unless you are planning to work hard to get a vertical branch transfer, go for NITs on the basis of your Mains rank or go for a drop. If your Open Rank is 3032, then you have a lot to choose from: - (The best options in no specific order, according to me are chosen as there are 50 and more branches open)
1] IIT Delhi Chemical (Dual Degree)
2] IIT Bombay Civil Engineering
3] IIT Madras Aerospace
4] IIT BHU Electrical Engineering
5] IIT Jodhpur Artificial Intelligence
6] IIT Guwahati Mechanical
7] IIT Bombay Metallurgical
8] IIT Bhubaneswar CS (5 Y) CS from all the newest IITs
9] IIT Indore Electrical Engineering
10] IIT Delhi Production Engineering
But if I were you, I had pick IITM Aerospace
PS - Data based on JEE 2020.

First of all, congratulations on your results. The JEE Main Cutoff for 2022 was recently released, and usually this cutoff is of two types: the qualifying cutoff and the admission cutoff. The admission cutoff for JEE Main will be the opening and closing ranks for each government institute like NIT and will be released by JoSAA (joint seat allocation authority). Based on the information you have given, you have fewer chances of getting into NITs or IIITs. Depending on the course-based cut-off, you may be able to get into institutes such as NIT Agartala for specific branches. However, you can try getting admission into government colleges in your state that accept JEE scores. For instance, some colleges in Telangana, Karnataka, and Rajasthan accept JEE scores. You can also use the Shiksha platform's JEE Main College Predictor 2022 (https://www.shiksha.com/engineering/jee-main-college-predictor) to get more specific recommendations based on courses, fees, and rank. Here you need to enter your JEE rank or percentile, gender, category, and domicile to get recommendations of possible good colleges.

The National Testing Agency NTA conducts the Joint Entrance Examination JEE Main to shortlist candidates for the JEE Advanced for admission to the Indian Institutes of Technology (IITs). Candidates must have passed or appeared in Class 12th or its equivalent from any recognised board to be eligible in the year of application. Since NIOS is also a recognised board, candidates are eligible if they have passed the 12th at NIOS. There is no age limit for appearing, and candidates can appear in the exam in three consecutive years from the year of passing class 12th. You attempted JEE Main in 2022, and you have consecutive chances in 2023 and 2024. In 2023, you'll have your NIOS marksheet, and, considering 2022 was your first attempt, you are eligible for JEE (Mains) under the NIOS board. You are not eligible after three consecutive years of passing your 12th. To get more clarity, you may visit the official website of NTA.