Theme: Pad, soldering point, via, plated-through hole
Drill hole not in the center of a pad?
Normally a drill hole or an oblong hole is centered to the pad. But you might select pad form "polygonal". So you can create the standard form of your pad as a polygonal pad.
Now you displace the pad a bit by an offset from the center:
(Image 1: Change pads, select polygonal shape of the desired primitive, and move the polygon a bit from the center)