I just got a forward handle longbow. I have a GN quiver on it. Iam left-handed. When I shoot the handle wants to twist clockwise. I use a Fred Asbell type grip with just thumb and index. The twist is less with quiver off. My arrows are hitting to the right a lot. I like the weight of quiver on bow. Anybody else experience this? Solutions?

Yep.  If you don't grip the bow a little more tightly, the bow quiver will cause the bow to rotate in the hand at the shot.  That's why a lot of folks don't like bow quivers.  Lighter quiver may help, but a GN is among the lightest to begin with.  A firmer grip is the only thing that will consistently straighten out your arrows.

Thanks Orion, I will try that. I spent a lot of money on this bow and Iam starting to wonder if I made the right choice.

I was never really clear on what constitutes a "forward handle" but I have a Life Ender that doesn't recognize an attached quiver. It shoots the same with or without. Dont give up on your bow, you will work it out.