My daughter has an almost identical space in her house. There is not really much to be done with it other than maybe a narrow bit of storage against one of the side wall.

It would be an alright place to keep, maybe, the vacuum cleaner. You already have some things kept in there. That all looks about right.

You don't need to fill up every space. It is alright to let some space just be space.

I would likely fasten some spring clips and hooks to boards and mount them to studs with screws. Use for storing things like broom and dustpan, bags of wrapping paper, etc. Generally things would be out of the way since they would be flat against the walls, but if need be, the boards could be unscrewed from the walls relatively quickly.

Nothing is quick when you have to empty a shelf and dismount it.

Don't put anything on the wall with any depth that will hamper your access to the attic. I doubt you need that little bit of storage space that badly.

I'd paint it and use it to store either a vacuum or Costco-size packages of toilet paper.

Why not a shelving unit on casters that can easily be moved out of the way.

It is on the stairs. Wheels would be useless.

The attic access in our house is in my walk-in closet - and the clothes rods need to come down to get a ladder to the attic. Fortunately I've only been up there a dozen or so times in the 30 years we've lived in the house (it is not suitable for storage), so it isn't that big a deal to move things out of the way.

What do you need storage for? This might be a perfect place for out of season clothes, which would not be hard to move if you had to get to the attic. Put a bar as high as you can reach, with no shelf above, so you can still use the lower part for tubs or a vacuum.

I'm curious to see how you end up using this space.

Sorry about that must have been too early. I think the best would be as mentioned just a good spot for cleaning supplies in a bucket and the broom and dust pan. If you don’t need storage don’t stress over this tiny little spot.

Not a Pro.

Paint the closet in your favorite color. Add a peel and stick saying to the back wall that makes you laugh. Store things in plastic containers that can be stacked, label them. (as mentioned by someone above.)

There seems to be room on the back of the door to add some narrow shelving

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I agree, don't stress too much over a bit of space. If you don't need the space for storage, let it just be. You don't have to fill up every bit of space with some clever and convoluted storage.

Personally, an empty space like that would make me smile every time I opened that door.

It seems that what you may have is a solution looking for a problem.

I saw something like this recently, and in fact posted a pic of it on a thread here--something about a closet under the stairs.

Anyway, someone had built a big box that exactly fit into the closet space, just leaving room underneath for some big casters. So they could pull the whole box straight out to access the space behind, without disturbing anything inside the "closet."

Theirs was more about being able to access stuff stored at the lower levels, where the angle of the stairs created space deep in the closet that would otherwise be unreachable.

However, you have that step at the bottom that comes all the way out to the doorjamb, so you don't really have a place for a unit to roll in.

Otherwise, I'd go with the idea to stashing the vacuum there, and out-of-season clothes in big plastic tubs that are easy to pull out.

and maybe back-of-the-door storage for things that you need to put your hands on quickly in that area.