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As mentioned, always check all the wires and connections first. A high resistance connection is a load just like a resistor so it will get hot and draw unnecessary current. The battery should be load tested, charged, and serviced unless it is a non service type. In any case it should maintain rated voltage well after charging.
If everything checks OK then it's time to think about an alternator repair or replacement. The solid state internal alternator controllers should keep voltage right on spec and current should be minimal after the battery is changed back up from starting the engine.