Bmw 523i 1999 model asc light on and stays on when driving ABS working normally

The fact that the ABS is OK means that the wheel speed sensors are OK. The sensors are the part of the system that get the most abuse, so it is good to eliminate them as suspects.
On a 1999, I think that you have a mechanical (cable-driven) throttle rather than drive-by-wire throttle. If so, the ASC has its own throttle just outboard of the regular throttle. If you don't see it, follow the air tube up from the air filter to the intake manifold. The throttle(s) are attached to the center of the intake manifold at the end of that air tube..
If your ASC has its own throttle, that means that you have an actuator and a little throttle cable running from the actuator to the ASC throttle. Since that is a moving part, it is subject to wear, dirt, and corrosion that interfere with motion. That makes this system the second suspect after wheel sensors. Check that cable for fraying and a full range of motion as it pulls the lever on its throttle. Unplug the control wire to the actuator and make sure that the connections are clean and tight.
I recently had an ASC light that turned out to be a hose clamp that was installed improperly and was interfering with the motion of the throttle arm on the ASC throttle.