After having this whole controversy with fans, the PlayStation 4 version of Fallout 4 will have mods for it after all. As we all know the PS4 version of Skyrim remaster already has them. Even though the PlayStation 4 mods will have limitations as opposed to the Xbox One version, it is still something the users can work with.
There are fans that hope the PS4 version can live up to the Xbox One mods. After being asked on Twitter,  Pete Hines, VP of Bethesda, said “we did that already. it wasn’t approved. whether it will change in the future, I don’t know. It isn’t up to me.” He also said on a later tweet that they will continue to push to push to have mods work the same on all platforms.
We will see what happens.
Source