I am currently imagining it as an attribute, but let me sketch the situation for this enhancement.
I often work with artists in my unity project, and most often our project structure works in a way where the root of a prefab acts like the script container, and basically references everything it needs to build up or set up that prefab and do it's things. And often i limit my assignable variables to something limiting so nothing weird might be assigned to it.
More the rule than the exception, we need these variables to be Asset/Prefab references. Any child of this prefab will do. Only sometimes an [AssetsOnly], rarely we make a scene reference or use [SceneObjectsOnly]. I am looking for something like [ChildOfThisOnly].
My original idea was that where the Unity Asset Picker shows "Scene" "Assets" tab, to add a "Prefab/Children" tab to just quickly find "particles" under this specific GameObject, because 9/10 that is the one item i am looking for (the picker is not helping me if i have to look through all eligible items) I often resort to just dragging the child object into the parent instead of using the picker because of this.
An additional benefit might be, that you can select a child object of a prefab, without actually pulling said prefab into the scene to make said change/assign (as it might be more than 2 layers deep, and we all know unity does not allow you to open up a prefab like that unless it is in the scene)
So all in all, this might be both a request for an attribute, and a request for a new type of asset picker, but i imagine the later will be quite hard to add.
Let me know what you think, or ask away if you need more info on it.