A rectangular plate with a Fixed Support on the end face is not a real design, it is an idealization and simplification of a real design that is easy to analyze, but includes a singularity.
What is the real design?
For a one piece part that is machined or cast, one real design is a base plate with mounting holes and a blend radius from the base plate to the integral cantilever arm.
A different design might have a base part with tapped holes. A long flat plate with clearance holes goes on the base part and cantilevers off the edge. A short flat plate with clearance holes sits on top of the cantilever plate. Bolts clamp the long plate between the short plate and the base part. A detailed simulaton of these parts can create a model where the highest stress in the cantilever plate does not have a singularity.
Finally, you could have two fixed cylinders, one on the top side of the cantilever near one end and another one on the bottom side of the cantilever a short distance inward from the first cylinder. Use Frictional Contact between the cylinder and the cantilever plate. This method of support does not have a singularity.