Jimmybr6

My battery went out so I replaced it check the charging system and while running it had 14.3 volts , so that good but after driving in the day time the gauge would drop to 12.8 volts shut the truck off start back up and the gauge would go back up. If I'm driving at night with the lights on it seemed to be ok. It's got a 120k miles so I decided to put a new alternator on it. Same problem . any ideas? I check the harness and it seems ok I also verified the voltage with my meter to. The battery light never comes on but it would always stay consisted at 14.4 volts before.