Smudged Corners when using Subdivision modifier

Question

I'm currently working on a scene, where I'm making some basic models (I have very basic modelling skills), and have a mesh made from a cylinder, that after making a few edits to, and applying a bevel + subdivision modifier to, results in this weird geometry:

I was able to drastically reduce that, by adding a loop cut, and increasing the subdivision level:

..but still wondering, what causes that kind of topology? Is it a common issue, that needs to be resolved with loop cuts or am I missing something?

Thanks in advance for whoever reads/replies to this 🙂

Edit #1

Tried the alternative technique suggested by moonboots, which works in keeping the corner sharp with the subdiv modifier, but also results in this weird topology:

Edit #2

I must have selected an extra diagonal edge in the previous attempt that created the ngon, but even after select the right edges (I think) I now get the following smoothing:

Answer 1

Because of your topology, the Subdivision Surface tries to round this corner:

If you choose this topology instead it will work fine:

Edit: As I said, you need to avoid ngons on round surfaces because it tends to create artefacts, instead stick to this kind of topology:

The problem with the topology that you show below is that there are still these 2 faces and the Subdivision Surface modifier tends to round the shape, therefore the artefacts:

See the difference between these two topologies, you need to choose the one on the right, it will be easier to rework and sharpen when you'll give it the Subdivision Surface modifier:

Answer 2

In addition to what others have said, A good rule of thumb when modeling in subdiv like this is to make sure you have plenty of geo to start with as well. You don't want to be going from a 16 sided cylinder to a 256 sided cylinder in one jump. Try to apply some subdiv modifiers in stages, or at the very least start from a place that is closer to your final result. Big shading distortions and lines on the side of cylinders is a sign that you are asking the subdiv modifier too much.

For example, this cylinder has literally no "special" edge-loops or crazy pro-level geo applied; it's literally just a cylinder with an inset. But since I'm only asking the subdiv modifier to smooth out the final result instead of do half my modeling for me, The result looks a million times better without even trying.

No subdiv Applied:

With Subdiv Applied: