Where is the fuchsia city gym?

The term "Fuchsia City" and a corresponding gym are not part of the official Pokémon games. It's possible you're referring to a fan-made creation, a fictional city from another media, or a misunderstanding of a real location.

To help me understand better, could you please provide more context?

For example:

* What game are you referring to? (e.g., Pokémon Red, Pokémon Diamond, etc.)

* What are you trying to find? (e.g., the location of a specific gym leader, the name of a specific gym, etc.)

* Where did you hear about this city? (e.g., a fan-made website, a friend, etc.)

With more information, I can help you find the information you're looking for.