Fallout 4 PS4 Mods are not going to happen officially due to Sony and Bethesda not coming to terms. However, according to Bethesda, they do have alternatives and are doing the best they can for PS4 players.
@MrMeeseeks187 I assure you we don’t lack for alternatives. We are trying to do the most possible for PS4 players
— Pete Hines (@DCDeacon) September 24, 2016
Sony denied approval for Fallout 4 PS4 Mods, Bethesda said:
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.
There are some ways that may allow Bethesda to bring us Fallout 4 PS4 mods. The company can consider doing this with console commands which can be activated in console games – Ark: Survival Evolved is an example of console commands in consoles.
Mods can also be added as free DLC for Fallout 4 via PlayStation Store. Bethesda has promised an update on the situation as soon as anything changes so stay tuned.
Fallout 4 mods are available on PC and Xbox One for now.