Of course it can be done! Use the Projection command in the Gen Shape Design workbench to project points (or lines or curves) onto a surface.
I'm not able to open the jpg image you attached. Could you try attaching it again, please
I'm assuming you want the points at specific coordinates on the surface, which is why I suggested the method of projecting sketch points.
The easiest way is to use the On Surface mode in the Point command. Just select the surface, click a location and OK to create the point directly on the surface.