About Arcade Controllers

Arcade Controllers is a broad category that encompasses the vast majority of third party controllers that are used for playing arcade games, arcade style games or fighting games.

As long as you can connect the arcade solution to USB, it has working udev/drivers and xinput then it should work with RetroDECK.

Always check for Linux Support
Just to be safe, it is better before you buy anything to double check if there is Linux support for it. Wireless Fight Sticks can be a hit or miss depending on if they require external configuration software.

Fight Sticks

Many USB Fight Sticks work nativly on Linux without much of a configuration. There might be need for a slight input remapping if they are a console version of a Fight Stick.

Fight Stick 2 Player Combo

Several suppliers have made Two Player Fight Sticks Solutions for versus and co-op gameplay.

Arcade Machines - DIY

There are several predone kits to make your own PC connected Arcade Machine.
They a majorty of them use a standard USB interface to connect to the PC and many times the same connector board as in the standalone Fight Sticks while the trackballs has a seperate USB connection that simulates a mouse.

There should not be any major issues connecting these with RetroDECK except maybe a controller remapping.