I'm not understanding the problem. It is possible for a gun to shoot high in relation to the rib or bead, and it's also possible for the gun to not fit you and shoot high for you when shooting flying targets. Identifying which we are talking about is essential to correcting it.

I believe that a shotgun should shoot true to the rib or bead. That means that if you aim it like a rifle the gun should center the pattern on the target. If it doesn't, something is wrong with the way the gun was built at the factory. Of all the problems to have, shooting high is probably the easiest to correct.

But it's very possible that a gun will shoot true to the rib, but then you shoot high when shooting moving targets. That can also be corrected, but we need to know which problem you have. Since you speak of aiming at the beard, it sounds like this is a turkey gun?