I installed new battery after checking alternator it sits with everything off

Yes the light came on three days after installing battery I have been disconnecting the negative cable when I am not using the car to keep battery from running down But yes the battery light stays on

Replace alternator!!!!!!

one last ? while car is running and I take off just the negative cable from the battery and the car still runs don't that mean alternator is still good? Thank you for all your help

At that time it's output is enough to run the engine however it still may not be charging! Not a good idea to remove the battery cable with engine running, ECM provides the regulator for the alt. voltage!!! Get a mechanic to test the alt. voltage output, not a parts store.