Hi is this a load bearing stud next to the basement staircase. It seems to be connected right near the joist and was concerned about removing it. My assumption is if it wasn't load bearing the builder wouldn't have constructed it from the ceiling joist to the basement floor.

Nope, it's there to attach the banister to only. That's the easiest way to secure the banister. It's not easy to anchor a post to the floor so it won't move if the top isn't tied to something.