Tenchi Muyo! Daughter of Darkness
The movie, Daughter of Darkness, was actually based off the 12th out of 13 novels written by Naoko Hasegawa, a scriptwriter for the first season of Tenchi Muyo! Ryo-Ohki. In it, a girl named Mayuka arrives and claims to be Tenchi's daughter and her origin and connection to Yuzuha (the antagonist in this film) is investigated. Sasami befriends and is a great advocate for Mayuka. In the finale of the film she is taken hostage by Yuzaha as she tries to protect her new friend.
Hasegawa novels
This film is the only contact most non-Japanese fans have had with Hasegawa branch continuity. The first book of the series, The Hexagon of Love, was produced with the cooperation of Masaki Kajishima and briefly considered original canon. The second and third novels retell the story of the first season of Tenchi Muyo! Ryo-Ohki. but afterwards branch off into their own direction which is sort of a combination of both the OVA and Universe canons. None of the novels have been officially translated outside of Japanese, so little is known about the character development within them.
Okuda manga
Sasami Manga
Two official manga series have been created by Hitoshi Okuda - No Need For Tenchi and Shin Tenchi Muyo! (aka The All-New Tenchi Muyo!). Based on the OVA series and branching off after episode 13.5. The manga series generally has a lighter attitude than the anime series and the characters personalities reflect this. Sasami has a much more open relationship with Tsunami-kami-sama, who herself is more breezy than her own OVA counterpart, possibly due to Sasami's influence, but more likely by Okuda-sensei wanting to write her that way. Sasami is the only person, in the manga or the anime, that Tenchi has said the words "I love you" to. In volume 5 of the second manga series, Sasami's age is given as 709 years, however, Sasami's age was returned to 708 in volume 7 of the second manga series for unknown reasons. Possibly a mistranslation in either volume.
Ai Tenchi Muyo!
A new continuity that mostly follows Tenchi Universe, with small differences. an experiment of Washu's has caused a big mess by displacing a couple Juraian travelers in space and time. Sasami, a teenager in this version, aids Tenchi as he tries to help fix Washu's mess.