Hello there. Hope you are doing good. I would like to tell you that NITs are not included in the list of institutions participating in JEE Advanced score accepting colleges. I am sharing a link with you which consist of names of all the JEE Advanced participating institutions.

https://engineering.careers360.com/articles/jee-advanced-participating-institutes

I hope you found this answer helpful. Good luck for your future.

Sorry but JOSSA don't provide this facility.

By jee mains rank you can only choose nits/iiits or sit in nit counselling and by jee advanced rank you can only choose iits or sit in iit counselling conducted by JOSSA. There is no option to get seat in nit with jee advance rank.