Battery light will not go out

2006 Ford Fusion

I have an electrical problem with my 2004 ford fusion.The battery light will not go out. replaced battery checked alternator it is a little low on voltage but car will run with battery cable is removed ,what could cause this?

Could be a damaged or faulty internal voltage regulator in the alternator. And to be clear, according to Wikipedia, the first generation Ford Fusion is from 2006.

So once I pulled up the wiring diagram for the 2006 Fusion I noticed a possible cause. It appears that the vehicle is equipped with two fusible links. This would cause your vehicle to no longer be able to charge the battery. Check these fusible links first. Should find them inline in the wiring close tot he battery.

2006 ford fusion alternator wiring diagram
2006 Ford Fusion alternator wiring diagram