Some TMNT stuff really isn't for little kids.
Because the Archie Comics-published comic series Teenage Mutant Ninja Turtles Adventures originated as more or less a straight adaptation of the 1987 animated series, Splinter once again originated as Hamato Yoshi, shidoshi of the Foot Clan.
As in the animated series, Hamato Yoshi loved Renaissance art, was tricked into being kicked out of the Foot Clan by Oroku Saki, and eventually mutated into a rat and witnessed four turtles mutate into humanoid forms after the five of them were exposed to mutagen.
When the comic stopped doing adaptations of cartoon episodes and started doing its own material, Splinter became a more active ally to his students Leonardo, Donatello, Raphael, and Michaelangelo and also began to teach April O'Neil ninjutsu.
The 45th issue of the comic, Mutations, retold Splinter and the Turtles' origins, but retconned a few elements so that the Turtles were still infants after their mutation and grew to teenage years as Splinter raised them as well as changing it so that Hamato Yoshi was kicked out by the visiting sensei Grand Master Yamaguchi after Oroku Saki framed him for murdering one of his own disciples instead of being accused of attempted murder when he removed a knife pinning his robe to the wall behind him.
The same retelling also revealed that Hamato Yoshi obtained the name Splinter when the young Turtles observed the stick he used when his mutant rat form made it difficult for him to walk and that the name of the rat whose contact caused his mutation was Ogata.
Hamato Yoshi was temporarily restored to his human form in The Year of the Turtle story arc, where he also told an amnesiac Michaelangelo who had just been restored to his mutant turtle form the story of the Turtles' final battle with the Shredder.