These were the first games he wrote after the wrestling games. These three games set the stage for Kill the Past and are generally considered the very beginning of the series, and characters from them would go on to play minor roles in Grasshopper Manufacture games.
The Twilight Syndrome series was actually continued by other writers following Suda's departure, most notably with Twilight Syndrome: Reunion. Said game is another sequel to the first two Twilight Syndrome games, and is considered the canonical sequel in the Syndrome series, while Moonlight Syndrome is the canonical sequel in Kill the Past, effectively splitting the timeline. Another game, Twilight Syndrome: The Forbidden Urban Legend was much later released for the Nintendo DS.
Around the release of the DS game, the franchise received spin-off works in other mediums such as the movies Twilight Syndrome: Dead Cruise and Twilight Syndrome: Dead-Go-Round, as well as a novel with the same two names.
Twilight Syndrome receives a notable reference in the Kazutaka Kodaka game Danganronpa 2: Goodbye Despair, in which the primary antagonist Monokuma develops a fangame of the series entitled Twilight Syndrome: Murder Case, which the characters (and therefore player) have the opportunity to play. The graphics, gameplay and story all invoke the classic series, and the game is vital in solving a murder mystery within Danganronpa 2. This is referenced again in the Danganronpa 3 anime, with the caption "beginning of the twilight" when the show begins to go over the events that inspired Monokuma's fangame.