Just reposting something I shared a couple of weeks ago (be advised a couple may no longer be available at MSRP):
I've gone overboard with my USB controllers, from RetroFlag for SNES, Hyperkin for Genesis, Hori for TurboGrafx, the PS Classic controller for PSX, Hyperkin for Atari, and a RetroUSB NES adapter for my original controller (there aren't many good 2 button NES style controller) ... and a crap ton more, ha.
Is this the one you got? Cause it seems to work the same as the other one to me.
Official Turbo Controller for Turbografx-16 Mini by HORI https://www.amazon.com/dp/B07V1Q2G8T/ref=cm_sw_r_cp_api_i_13CXEbAEGPKMV