This is a smal piece and I want to add 2 or 3mm thickness. During the process I notice that the thickness on the edge is being projected to outside the model. I have tried a lot of configs but without good results.
The Offset property on the Solidify modifier is probably doing that.
With a value of zero, it will add the thickness to both sides, centered on the plane.
Setting it to +1 or -1 with make it apply the thickness to one side or the other.
+1 will push the thickness out from the front of the plane. -1 will push it back, and only add the thickness to the ‘inside’.