There may not be a widely known single 'adam levine horror story'. However, if it's about some negative incidents in his career, like the cheating scandal that came to light some time ago, that could be considered in a sense a 'horror' for his public image. But it's not a traditional horror story. It was more about his personal conduct and how it affected his public perception and relationships.
I haven't heard anything about Adam Levine being part of American Horror Story. Usually, casting announcements are made by the show's producers, and there haven't been any such announcements regarding him. It's also important to note that the show often features actors who are known for their work in horror or have a certain acting style that fits the mood of the series, and Adam Levine is mainly known as a singer rather than an actor typically associated with horror.
One possible interpretation could be if there was a story where he was involved in a spooky or disturbing music video concept. For example, if the video had elements of the supernatural like ghosts or demons and Adam Levine was at the center of it, that could be seen as a horror - related story.
There is no information indicating that Adam Levine has been part of a sex scene in American Horror Story. Adam Levine is mainly known for his music career, and while he may have made appearances on the show, it's highly unlikely he was involved in such a scene.