Is there any government college still providing admission for B.Tech? I have 1 years' gap between my studies.

Now, it is not possible. If it is too urgent, then you can prefer Gopeswar Government College, which also has good academic reputation.

Government college dates at this time is not available, but yes you can opt for the Institute of Technology, Gopeswar. It is a government college, and it offers admission on the basis of class 12th marks also.