sr = arcpy.SpatialReference (...spatial reference info...) #spatial reference object
moveLyr = "SnapToMeLayer" #layer to be snapped to edge or vertex

class MoveLeak (object):
    def onMouseUpMap(self, x, y, button, shift):
        point = arcpy.Point (x, y)
        clickGeom = arcpy.Geometry ("POINT", point, sr)
        arcpy.CreateFeatureclass_management ("in_memory", "pnt", "POINT",
                                             spatial_reference = sr)
        tempPntFc = r"in_memorypnt"
        with arcpy.da.InsertCursor (tempPntFc, "SHAPE@") as curs:
            curs.insertRow ((clickGeom,))
        #snap 6 feet distance used to allow wiggle room with click
        arcpy.Snap_edit (tempPntFc, [[moveLyr, "EDGE", "6 FEET"]])