JEE Scores

You can check following colleges:
1-School of Engineering, Tezpur University
2-Institute of Technology, Guru Ghasidas Vishwavidyalaya (A Central University)
3-Shri Mata Vaishno Devi University
4-HNB Garhwal University
5-National Institute of Foundry & Forge Technology
6-Institute of Technology, Guru Ghasidas Vishwavidyalaya (A Central University)
7-Mizoram University
8-School of Engineering, Tezpur University
9-Sant Longowal Institute of Engineering and Technology
10-School of Engineering, Tezpur University

You won't get any college through JOSSA. I would recommend you to look for a good private college.

If you have got that category rank then sorry you won't get any NIT for core branch though you have chances to get some decent government college in last few rounds.

You can consider following colleges:
DIT University
Alliance College of Engineering and Design, AllianceSchool of Technology, Pandit Deendayal Petroleum UniversityJECRC University

You will not be able to get any Government Colleges and there is very less chances of getting Government college in your state also. But you can get Private Colleges with these Marks.

RGIPT, IISER's IIPT are one the best colleges you can get through JEE Advanced othet than IITs.
All the best.

For JOSAA, you have to apply through JEE Mains and for WBJEE counselling, you have to apply through WBJEE.

You're chances are slim. Though you should apply to some other college as you're from st category you have chance to get some government college. All the best.

If the score you mentioned i.e. 119 is of JEE Mains paper 2, then you cannot get NIT anywhere. Although with such a good percentage in boards you are eligible for getting admission in other B.Arch colleges in your area. Check last year's cut-off and assure your seat for college. Good luck :).

Check out the college predictor link below for details : https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.