Points attached to a prefab

I am making a puzzle game where each piece is a prefab. It kind of works like pipedream, so I plan to draw lines on the pieces. The question is how do I link points on each 3d model of each piece per prefab? Ideally, I would like to do it with Vector3 's , but any way to describe 3d points would do.

Alternatively, is there a way to do that in blender? If so, how would I access those points?