Sub-D problem with edges I want this edge to be hard, but when I try to use the bevel modifier or edge crease, this problem occurs. Also when I tried to add support edges, it still looks bad and creates other unwanted problems with the mesh.

Can you help me fix this?

EDIT: Topology



EDIT2: Curved Part
What you want to do is switch the Outer Miter from Sharp to Arc. This will solve your problem without having to bevel any additional edges that might break curvature.



If you want to end up with geometry that's still all quads, you need manually triangulate the pre-bevel quads that buttress the bevel-weighted corners, as follows: