The following links point to the latest stable version compiled for macOS_ARM64. These are 3.1.x versions based on slightly newer code than the 3.0.5 version.

FS-UAE-Launcher_Stable_macOS_ARM64.dmg
FS-UAE_Stable_macOS_ARM64.dmg

Compared to previous downloads, FS-UAE Launcher.app no longer contains an embedded FS-UAE.app. Therefore, you need to download both of the .dmg files above and place FS-UAE Launcher.app and FS-UAE.app beside eachother, for example in the /Applications folder. I haven’t had time to fix builds of FS-UAE Arcade yet.

There are also macOS_ARM64 builds available for the 4.x development snapshots. If interested, please see this forum thread for links and more information.