Off and hanging next to me.

Do whatever you're comfortable doing. If your bow is more quiet and you feel comfortable shooting without the quiver, shoot without it

I'll bet that more people here have had second shots than they are willing to admit. I have missed before and curiosity brought the deer back real close, thats how I got my 1st last year.
That being said, I remove my quiver when I get settled in, I hang it on a rubberized bicycle hook and have no problems quickly grabbing for another if needed.

Quiver on. Mine is not detachable. I used to remove it on my old bow. I haven't noticed any shooting diference but I think the bow might be a little quieter with it off. Especially when shooting expandables.

i leave mine off. dont need extra weight and or anything that can catch the wind at full draw and it helps eliminate any extra noises.