Your short pitches around the green end up right of your intended target, or they skip across the green because you catch the ball thin.
Because these are short shots with a definite target, there’s a natural tendency to help the ball into the air by moving your club up and to the right. You swing “under” the ball rather than through it, which causes the clubface to remain slightly open at impact, sending the ball right. Solid pitches result from trusting the loft of your club to get the ball into the air and swinging your club on a full arc by moving both the clubhead and the handle to the left of your target through impact.
Think “arms” on these shots. If you use too much hand action, you’re likely to shove the club to the right then flip it over to the left. That’s a recipe for sculls and shanks. Don’t change your address position or your backswing, but use your arms to swing both the handle and the club to the left of your body following impact. This will properly square your clubface for extra-crisp contact.