If you've got the same issue I have, then let me save you my fourteen hours of frustration. The Collector's CD version of TIE Fighter (by far the superior one) had a glitch in the joystick controls 'when using the Microsoft Sidewinder 3D Pro, the Suncom Raptor, or other joysticks which may incorporate controls using axes from joystick 2.' There was a patch published in 1996, that thankfully you can still get at archive.org
here. Download that, copy the 'Z_TIE__.EXE' file to the install folder, overwriting the version that's there. Voila! Working joystick controls!
If you're using one of the other two versions of TIE Fighter, then I can't help you, sorry. I'm just SO glad someone on a Discord I'm part of remembered this patch from
TWENTY-FOUR YEARS AGO and it solved all my problems. Hope it helps you, too!