New battery new alternator gauges still read the same no change engine kill batt

What is your question?

I've had a new alternator bench testing the batteries charged fine but I pull the plug off the battery in the battery cuts out the engine doesn't run smooth I pull the battery fuse and the lights go away in the engine runs better but I pull the battery terminal and it still cuts off I don't know what to do I'm looking for advice this all started when I was accelerating the motor would cut out all the idiot lights would come on and the motor to cut on and off so I change the fuel filter and then this problem happen