Is there a final exam on the third semester?

I've searched on the internet, but nothing pops up that there is a final exam on the third semester. The first and second semesters have final exams, but I have no information for the third semester.

The third semester of what?

Third semester of high school

Every school semester is supposed to end with final exams. Whether a school has three semesters or only two is a different story.

Then on the third semester of high school, january to mid-march if I'm correct, when are the final exams held? Based on what I've read, the first and second semester final exams are held on the last month of the semester so is it the same on the third?

final exams are held on the last month of the semester so is it the same on the third?

Yes. During the final exams students go home before lunch just as they do during mid-term exams, and there are no classes after final exams, except for some extra classes that some students may need to take.

third semester of high school, january to mid-march if I'm correct

Technically that is correct on the calendar, but in reality, there are a lot of events on March such as the graduation ceremony, entrance exams for next year's freshmen, and entrance exams for those aiming for college. So final exams often start as early as end of February and continue on to March.

But again, these are just basic facts. In reality, students in their last year of high school may not have final exams, and private schools may have different policies. Details can be found on Japanese language Google.
https://www.google.co.jp/search?q=%E9%AB%98%E6%A0%A1%E3%81%AE%E6%9C%9F...

There are, by definition, only two semesters in a year, so the third semester would be the first semester of the second year?

the third semester of high school, january to mid-march if I'm correct

??????

I don't think the word "semester" means what you think it means. A semester is, etymologically, a period of six months. In common usage it just means "half a year", which is usually the same thing but can be different depending on what "year" means in the given context.

Okay, I always felt that what we call "gakki" in Japan is the same thing as what we called "semester" when I was going to school in the U.S. And some schools in Japan has 3 gakki per school year while others have 2 per school year. Anyway, the OP says the question came just out of curiosity.

Sorry, I just realized my question was not supposed to be "Is there a final exam on the third semester?" It was supposed to be "Is there a final exam on the third term of a trimester?" I just learned how to use "term" effectively yesterday; I'm such an idiot. Either way, it turns out that Uco understood it!