Before submitted that question I have made quite extetensive research and could not find the answer. I am quite new to Blender so I believe there is a chance the answer to my question might be simple but due to my lack of experience with Blender I did not recognize that.
The problem seem to be simple yet it is pretty complicated for me especially that I am trying to do beveling in non destructive way.
I have a simple plank with excision on one side. The excision was made in destructive way but the beveling is applied through modifier with weight kimit method (I am using speedflow and fluent).
Then what I am trying to do is to apply small bevel (about 1 mm) to all edges of the plank except four of them which are adjacent to one face.
I can - using bevel modifier - apply that additional beveling to all edges using angle as limit method but I do not know what to do to keep the selected edges sharp.
Not using any limit method (None) creates strange artifacts
While it is impossible to use vertex group as the edges I want to keep sharp are between verticies which are also part of the other edges that I want beveled.
----- EDIT -----
I have tried the method suggested by Merlin - applying bevel weight to individual edges - but it only works with simple geometry.
With more complex geometry it creates artifacts again.