So many different examples of this, but let's provide some examples

Godzilla NES: Probably one of the more recognizable and acclaimed horror fangames/creepypastas. Given Godzilla itself is already, when it's in its more serious films, pretty horrifying as the films can be shown to depict its themes, the creepypasta certainly lives in its place as a horror fan concept that has made its place among the community while not diverting itself too far in showcasing a creepypasta in the tune of the King of the Monsters, including new kaiju designs in the NES style, and a unique one, Red, being a malicious force-of-nature in the story. 

Sonic franchise: The amount of horror-related fangames, media, and creepypastas Sonic has is so plentiful since the inception of Sonic.exe, it is unavoidable to take about the franchise without that, for better and worse.

Mario franchise: While not as plentiful as his old rival, Mario has had a fair few too many horror fangames that emerged in the post .exe years, with there being multiple fangames and remakes of such fangames.

Kirby franchise: While not as numerous as Mario or Sonic, there have been enough Kirby fangames that bring the puffball into a horror limelight, which is ironic when you consider how the official franchise, at times, has several horrific concepts and elditrichesque designs in its years despite being on the model of a kid-friendly franchise. 

Cyclus Mortis (Yoshi.exe): One of the rare remakes that overhauls and brings a decent bit of gameplay from the original, which is itself a fangame of Yoshi's Island. It serves as a solidly built fangame with multiple endings, and unique ways to depict its horror through its gameplay.

And I'm totally sure no kids were ever traumatized from witnessing any of these videos or games (wink, wink I was one of them).

[Common as Horror Trope] A franchise gets a horror-based fangame/creepypasta/media/character