Hey Saswat,

You cannot register for state government engineering colleges in Odisha through JoSAA counselling.

For admission, candidates need to register for OJEE counselling through website www.ojee.nic.in 

After registration, candidates need to fill the preferred choices where they would like to get admission. After the registration, candidates will have to get their documents verified at nearest OJEE nodal centres. After successful document verification, seats will be alloted. The allotment of seats in preferred college and course depends on the availability of seats, merit and preferred choices. 

Hope it helps, good luck!