Battery light staying on after brand new alternator changed out please help

What is year--make--model?
If something wrong with wiring circuit, somewhere, replacing the part won't fix it.
Make sure charging system is working properly. To look up wiring diagram, I need vehicle info. The battery lite is on even with key out? Unplug alternator, see if light stays on, check the alternator wiring connector.

You may have a bad diode in the alternator. Or bad connection somewhere. Is the new battery draining?

was the alternator bench tested? or tested on the car? if the alternator tests good off the car and the wiring has been tested, the ground may be loose or disconnected.

Brother Mark, changing the battery with a new one being done won't make the light go out, as you noticed. Light is still on so you changed the alternator. Good, but the battery light is STILL on. This only means that the charging circuit from the alternator is not working in the voltage regulator or the wiring is not connected properly to the alternator/regulator. A new battery will show over 13 to 13.5 volts not connected. An old battery will still show 12 volts and still be weak or bad. After connected and engine running, the system will show at least 14 volts because alternator/regulator is working properly, using a voltmeter/load tester connected to the battery. If after replacing the battery and alternator it is still reading 12 to 13.5 volts, it is not working and the light will stay lit on the dash. You may have purchased a faulty alternator if the system tests out this way. Have your system checked with a volt meter or load tester bit be sure all the connections are proper and clean.

Look for a big red wire thats connected to the big post on the starter.Follow that wire up to the alternator. That wire should have battery voltage there all the time. If it does not, check that the fusible link, which is in that wire is not burnt or broken.

14.5V output. is to spec on a new alternator
at rest battery will be 12 volts
whats the problem

Something is staying on while its not running, could be a light somewhere that should be off thats not. With a good alternator and a brand new battery there should be no reason for the battery to just die within a day unless something is staying on. Pin point what is staying on and we can go from there

The FuseLink is blown. It is a 100 AMP in-line fuse on the red wire from the alternator.

Altinator is faulty.