Move the lens aperture ring to the minimum aperture point and the warning will probably disappear. There is probably a lock tab on the lens available to keep it there too. In this arrangement the aperture is adjusted with the thumb wheel.
This is a non-starter in this case. I always have the lenses set/locked this way (unless in the field I want to control things), still gets the fEE.

In the custom settings menu you can choose to set aperture with the ring rather than the thumb wheel. In this arrangement the aperture ring is left unlocked and there is also normally no fEE warning.
I'll give this one a try. Found an on-line PDF manual for the F100 and I'll spend some time with it as well. I have determined that none of my Sigmas work on the F100; 24mm, 28-70mm, nor the 70-200mm though all are quite happy on the N90s.