Hi aspirant, since you have 6957 OBC category rank so on behalf of this below are some of the NIT's or other government institutions where you can decide to take admission;

• NIT, Agartala
• NIT, Rourkela
• NIT, Hamirpur
• Central University of Rajasthan
• NIT, Durgapur
• NIT, Sikkim
• IIEST, Shibpur
• NIT, Imphal
• NIT, Shillong

Etc.

For more colleges you can take help of below mentioned link;

https://engineering.careers360.com/jee-main-college-predictor?utm_source=qna&utm_medium=jee_cp

Thank You.