Is there a way to change our course in NIT Trichy after first year?

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.