I understand now. It’s the Subdivision that’s the issue.The bevel width is too small for the subdivision to give a clean transition. If the aim is to have a softer transition between the cylinder and the protrusion, but sharper protrusion edges, like this:
I had to use a vertex group that excluded the front vertices of the extruded part as part of a ‘corrective smooth’ modifier. You’ll have to play around with the values of the bevel and the smoothing to find the sweet spot before artifacts appear.
Here’s the Blend file if you want to see what my settings are:
Bevel_and_SubDiv.blend (767.6 KB)
If it’s just to have a generally higher smoothing across the entire mesh, then tweaking the bevel width is the quickest solution.
Best of luck,