No, after the first year it is certainly not possible to change branches in NIT Trichy. You will have to stay in the same department which you will be allotted during the JOSAA counseling. 

But there is an internal sliding in all NITs after the completion of allotments where you can change your department in a particular branch. For example, if you are assigned Production Engineering, then you can move to Instrumentation and Control Engineering as both of them are under the electronics branch and the syllabus for both of them are similar.

So, what you can do is look up the allotment list for closing ranks of each department and try to estimate whether or not you will be eligible for internal sliding. Usually, the top 5 rankers (opening rank) from each department are eligible for internal sliding. However, this number varies depending on the people applying and the vacancies in a department. 

One of my friends had been a student of NIT Trichy, pursuing B.Tech. Let me share what I gathered from him and some reviews online.

• The excellence of the courses may vary in each semester, but according to my friend, there are a few courses that are never out of standard.
• Based on their learning opportunities, infrastructure available, extra-curricular/technical club opportunities, and internships and placements, these are some of the undergraduate courses that are considered best.
• The courses include - 
  • Computer Science and Engineering, 
  • Electronics and Communication Engineering, 
  • Mechanical Engineering, Electrical and 
  • Electronics Engineering is considered better.
• Keep in mind that you should always take the courses that are interesting to you.
• Thus, if these courses don’t intrigue you, you can go for other courses as they will be better for you if you are interested in them.
   

Many students have gotten to know about their field of interest while studying in college. Hence, give some time to figure it out and then make a decision, as this will shape your career further.