I am trying to snap a vertex to the position of another vertex but on the Z axis to its right above it.
I remember doing this back the days I started 3D stuff but forgot how to do it.
Press "s" on your keyboard to toggle the snap feature on and off. Right click the snap icon in the main toolbar to choose which elements are snapped to. Left click and hold the snap button to choose the range of 3D space to apply snaps to (2D, 2.5D or 3D).