2011 Fiesta SES electrical issue
 

My problem is the battery light came on so then went and had alternator tested and results was it wasn't charging so went and had it rebuilt then re-installed and was charging but that pesky light would not go out! With car not running ok then crank and starts fine with no battery light but 20 seconds later boom light comes on so stop it start again boom here comes that light when the light comes on it pulls the motor a little but nothing major but it does it every time also u can turn the rear defogger on and its fine then battery light comes on then the rear defogger goes off and will not come back til ya turn car off then start it battery light comes on rear defogger goes off every time. I checked cables and connections and all the fuses I know to check but none are labeled battery, alternator, or charge! the rear defog fuse is ok! anyone know whats up please help

This is a shot in the dark, but it could involve the BCM (body control module) or possibly the instrument cluster itself. It will require a capable scan tool to see what is happening and where the problem is originating.