Hello,

As long as you are qualifying an exam equivalent to Std XII from a board recognized by National Testing Agency, You are eligible to sit for the entrance exam for a seat in NIT. Since you have enrolled for the Integrated Btech program, you should check for the eligibility with the officials in NTA.

In my experience, IIIT Basar is a recognised college and its second year GPA should be enough for you to sit for JEE Mains. I would suggest you to first check for the University with which your college is associated and the search for it in recognised boards in Information Brochure. If not found, an official mail would be appreciable. 

Hope it Helps.