I have a Bejamin .177 pellet gun center break gun. It also has a Century variable scope. I had the shots on a quarter at 20 yards. I noted the focus was off a bit and sharpened it with a half turn. The next three shots were hitting in the 5 o'clock area 4 " away. I rotated it ccw towards where it was earlier, and it started to walk back to center in an arc fashion. Your thoughts?
I wouldn't think the focus ring would have anything to do with the point of
impact. I thought the mounts must be loose and began grabbing the scope and attempting to wiggle it. No movement.

 

It is possible the optic you were turning wasn't perfectly center trued, or not seated perfectly. That could account for the parallax against the cross hairs.

 

I was only focusing & a small amount of zoom picture. No adjustment on the crosshairs. Those are top and right, the focus and zoom are fore and aft.

 

The focus ring is independent of the reticles. The lens in the focus ring is what I was talking about being asymmetrical, and changing the parallax of your view through the tube. If it is an expensive scope, return it.

 

Cheap scopes can have issues/problems that more expensive scopes do not. You may have to adjust your focus then go through the process of re-zeroing. Then don't touch the focus again unless you plan on checking and resetting the zero. You may also find that each click on the barrel does not move the impact point the same amount and going one click forward then one click back does not return you to the original point. With cheaper scopes I will only adjust one thing at a time then take a few shots to let the internals of the scope move and settle where they want. Then make another adjustment and take a few more shots.

Also, spring powered air rifles can be very hard on scopes. Even harder on them than many rifles so don't be surprised if your scope slides in it's mounts or looses it's zero.