Skyrim Special Edition will be out next week on 28th October bringing console mod support to it, but there's a catch...
On PS4 mod reserve space will only be 1GB, Bethesda has confirmed. That's a little more than the original 900MB limit Sony had imposed, but not much. Comparatively, the Xbox One version will allow 5GB for mod reserve space.
That being said, many believe that 1GB will be more than enough space for the PS4 version of Skyrim as it won't allow mods that use outside assets. So no Thomas the Tank Engine dragons here, folks. Instead, you'll have to make do with assets already in the game. These tend to be very small, sometimes under 1MB, as they mostly consist of new text while the core assets are already installed. In this sense, it's more like a level editor with the ability to add questlines and dialogue rather than the sort of game-changing mods people are used to on PC.
The size limit could be more of an issue on Xbox One, since there's going to be a lot more available for Microsoft's console, which allows external assets. Still, 5GB is noticeably bigger than the 2GB restriction in place for Fallout 4, so it's definitely an improvement.