Which tribe was not counted with the others in the census of Israel's fighting men?

Answer: Levi

The LORD told Moses not to number the tribe of Levi with the other Israelites in the census.

“The Levites, however, were not numbered along with them by the tribe of their fathers. For the LORD had said to Moses: “Do not number the tribe of Levi in the census with the other Israelites.”— Numbers 1:47-49 (BSB)