should i fill form for private college or university before jee mains results 2021

Yes you should apply for various good colleges that takes admission on the score of jee mains but do not participate in JOSAA counseling. Some of these colleges are even better than new iit's and nit's. Names of colleges whose form needs to be filled before jee mains result are given below:
1. IIIT Hyderabad
2. IIIT Bangalore
3. NSIT
4. Delhi technological university
5. Thapar institute of engineering and technology
6. Indraprastha institute of information technology, delhi

Hope this helps