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. It turns out that Yuzuha's real target is Yosho, who she holds a misplaced grudge against. In the end Tenchi has to protect Mayuka and Sasami, whom Yuzaha ends up kidnapping.
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
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.
Ai Tenchi Muyo!
In a new continuity that seems largely related to Tenchi Universe, with small differences, Tenchi is now 22 years old and is cleaning up after a rather major mess caused by an experiment of Washu's. In an effort to save a couple time and space displaced Juraian travelers, Tenchi finds himself assigned as a student teacher in an all-girls school where the two have landed but have only the vaguest memories of their past. He needs to gather the two together and figure out why a previous attempt to fix things didn't work.