A surprising number of recently published science-fiction tabletop RPGs contain original settings modeled after classic science-fiction franchises, just as classic fantasy RPGs like Dungeon & Dragons are modeled after The Hobbit, Conan The Barbarian, and other fantasy classics. Fans of science fiction franchises like Star Wars, Mass Effect, Cowboy Bebop, or Alien can use the rules and original settings of these following tabletop RPG systems to tell stories that are similar in theme and feel while going in new, surprising directions.
Fan-fiction - that is, the art of borrowing characters and themes from the stories one loves to create brand-new tales - is a practice as old as the art of storytelling itself. Dante's The Divine Comedy was essentially self-insert fan-fiction where he and his favorite Roman poet Virgil went on an Aeneid-inspired tour of Hell, Purgatory, and Heaven. Garrett P. Serviss, a fan of H.G. Well's The War Of The Worlds, wrote an un-authorized sequel where Thomas Edison invents a disintegrator ray and a fleet of electric spaceships to strike back against the Martian invaders. The Star Trek fan community popularized the art of fan-fiction writing as an act of appreciation for cherished franchises, while Dungeons & Dragons, the first roleplaying game, was in some ways a system through which players could collectively tell stories inspired by their favorite sword & sorcery stories.
The following tabletop RPG systems were most definitively inspired by people who were fans of certain science fiction franchises. Their settings and rules, though original, are designed to help players tell stories in the style of the sci-fi TV shows, movies, and video games they love. In many ways, these original-setting RPGs offer more chances for good storytelling than official RPG adaptations do; players of these games don't have to worry about contradicting the pre-established lore of their favorite franchises, and don't have to cling to aspects of the franchise that are awkward or restrictive.
Galactic 2e (Inspired By Star Wars)
Galactic 2e is a science fiction roleplaying game described on its itch.io page as "a game of rebellion, relationships and war among the stars." Wholeheartedly inspired by the Star Wars franchise, Galactic 2e has character playbooks for archetypes such as the "Scoundrel" for Han Solo-type characters and the "Nova" for Jedi and Sith-type mystics. Built off of the "Belonging Outside Belonging" system used in the community centered RPGs Dream Askew and Dream Apart, players trigger "Weak Moves" that place their characters at a disadvantage into order to gain in-game currency to succeed at actions later on with "Strong Moves."
Into The Black (Inspired By Mass Effect)
Into The Black, according to Dicebreaker, is "a love letter to Mass Effect without the military trappings," set in a future world where space travelers in debt to powerful mega-corporations trawl through the depth of space to complete mission assignments and clear their debts. The three main classes in Into The Black are Soldier, Specialist and Technican, each with special abilities inspired by the soldier, engineer, and biotic classes from the Mass Effect franchise. Mechanics-wise, Into The Black borrows a lot from the Old School Renaissance school of RPG design, particularly more minimalistic games like Into The Odd or Electric Bastionland.
Orbital Blues (Inspired By Cowboy Bebop)
Recently funded on Kickstarter, Orbital Blues is a science fiction space western RPG about interstellar ruffians with a battered spaceship making a living across the lawless frontier of outer space. If this premise sounds familiar, that's because it matches the plot-lines of the TV show Firefly, the Guardians Of The Galaxy movies, and the Japanese anime Cowboy Bebop.
The simple narrative rules of Orbital Blues are designed to facilitate gameplay where a crew of misfits pool their skillsets to tackle legally dubious jobs and gigs, while the grungy outer-space setting is themed after Rock'n'Roll and Folk Blues tunes.
Mothership RPG (Inspired By Alien)
The go-to RPG for players looking to tell sci-fi stories of horror and suspense in the style of Alien, Mothership RPG is about groups of blue-class space travelers trying to survive in the harsh and deadly environment of outer space, filled with hazardous planets, deadly monsters, and endless dark. The main character classes in Mothership RPG - Scientist, Teamster, Android, and Marine - correspond to iconic characters from the Alien movies, while the game's D100 dice-centered rules, readily accessible on player character sheets, encourage games sessions filled with tension, terror, and copious amounts of lethality.
Sources: Mothership RPG, itch.io, Kickstarter, Dicebreaker