Hey there
For admissions into IITs or NITs you need to appear for a national level engineering entrance test called JEE mains. You have to clear cutoffs in order to appear for jee advanced. From jee mains score NITs take admissions and from jee advance score IITs take admissions. EWS quota and girl quota is valid during admissions
https://engineering.careers360.com/colleges/list-of-top-iit-colleges-in-india
https://engineering.careers360.com/colleges/list-of-top-nit-colleges-in-india
Good luck
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