With an OBC rank of 137081 in JEE Mains, the chances of getting into NITs or IIITs are slim, but not impossible. You'll likely need to consider newer NITs and IIITs, and potentially GFTIs, for a higher chance of admission.

Recommendations:

Explore JoSAA counselling options

Consider CSAB spot round

Don't limit yourself to top institutions

Be open to different branches

Check college predictor for more accuracy:

https://engineering.careers360.com/jee-main-college-predictor?utm_source=jee_main_cp&utm_medium=GoogleAds&utm_campaign=1001&gad_source=1&gclid=Cj0KCQjwtpLABhC7ARIsALBOCVopb0fzHqKi9HY6QW8OpByUto8-_talWB-R1XaaE48gPR0YMdLcYF0aAqShEALw_wcB