In most of the engineering colleges, the syllabus in first year is almost same for all the branches. So, it is possible sometimes to move straight from one college to another.
You can change your college after first year, but you can only go to a college which is under the same university as your present college.
Some documents ( migration certificate,  NOC) will be needed there definitely. You have to follow that.

Hello student,

Yes, you can change college after 1st year.You can join colleges that provide B.tech(lateral) admission. It depends on some factors like availability of seats in the branch you are interested in and your Cgpa in 1st year. Generally they are based on JEE Mains score, but, some colleges have different exam too.Above sceneario is to give admission to you in second year.You can also give exams like JEE Mains,BITSAT,IPUCET next year and if you get better college then you can go for it by dropping your current college. 

Hope this will be helpful...