In a bizzare twist, Sony has decided to axe any chance for running mods with Skyrim Remastered and Fallout 4. Despite earlier claims that they would allow mod support, it seems like they slammed on the brakes, while their main competitor, the Xbox One, is currently hosting mod support for Fallout 4.
This could only be a temporary setback, and I highly doubt Sony would fall behind like this without a reason, so I would not give up hope. This news comes straight from Bethesda in a post from their website. See below.
"After months of discussion with Sony, we regret to say that while we have long been ready to offer mod support on PlayStation 4, Sony has informed us they will not approve user mods the way they should work: where users can do anything they want for either Fallout 4 or Skyrim Special Edition.
Like you, we are disappointed by Sony’s decision given the considerable time and effort we have put into this project, and the amount of time our fans have waited for mod support to arrive. We consider this an important initiative and we hope to find other ways user mods can be available for our PlayStation audience. However, until Sony will allow us to offer proper mod support for PS4, that content for Fallout 4 and Skyrim on PlayStation 4 will not be available.
We will provide an update if and when this situation changes."