"THIS IS THE PLACE - J." proclaimed a hand-painted sign in a cave which Beau Maverick stumbled upon in the 'Maverick' episode "Red Dog". It was a sign to some desperadoes that they had reached the meeting place where "J" would reveal his plan for them all to partake in a big score.
As Beau soon discovered, "J" was a man named Jess, according to the others. But at the end of the adventure, he asked Judge Reese exactly who Jess was, and the old rake slyly dropped the full first name as "Jesse". It was an inference that Jess was none other than Jesse James.
But it was the Judge who forged the letters urging the meeting, in hopes of taking in all three outlaws for their various bounties. So it was a form of Famous Individual Syndrome, in which somebody impersonates a famous person for their own benefit. It's something that happened quite often to the reputation of Jesse James in Toobworld.
For example, here are two bumblers who tried to pass themselves off as Frank and Jesse James only to run afoul of a 20th Century reporter and a stranded Martian.....