I'm not sure what you mean by zig zag, but this would be a good spot for a spine bookcase.

That corner is not an optimum location for anything. Find a new location

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Could you put a skinny bookcase perpendicular to the closet door wall?

Don't put anything all the way to the end of that wall. The very narrow door needs to go all the way to the wall in order to fully open, and sticking something just in the tiny corner won't look right. If you want a bookshelf, put a lower one to the right of the door, or a taller one on the full wall to the left of the door.

What space is this? I'd just put a piece of artwork on that wall.