Hello Aspirant, hope you are doing good.

So, the admission in B.Tech colleges in Odisha government college is done in the same way as any other college in all over India, through your JEE Mains rank. Choose the B.Tech college you desire and check if your JEE Mains rank matches with the cutoff, if it does, you can get after the counselling rounds. There are state level examinations as well, like OJEE , which is also a way to get in the government colleges. You can get a list of all the government colleges in odisha, here:

https://engineering.careers360.com/colleges/list-of-engineering-colleges-in-india

If you want to know the entire list of all the colleges you can get into with your JEE Mains rank, you can get it here:

https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer

Hope this helps you. Good Luck!!