No, you cannot choose the same department in the same NIT twice under JoSAA counselling, once under home state quota and again under non-home state quota. JoSAA's system treats these as duplicate choices and will only consider one of them.

JoSAA aims to give students the opportunity to explore as many options as possible. By including the same department twice, you're essentially blocking a slot for another student who might have a genuine preference for that specific department-quota combination.

NITs have a limited number of seats available under each quota (home state and other state). Including the same department twice doesn't increase your chances of getting that seat. It just takes up space in your list that could be used for another department or institute you might be interested in.

I hope it helps!