When NBC tried to revive the 'Bonanza' franchise with TV movies, there was hardly anybody left to return to their old roles. Lorne Greene had been willing, but he died before he could be involved. Michael Landon was busy with his own show, 'Highway To Heaven', and Pernell Roberts knocked the dust of 'Bonanza' from his boots many years before and never looked back.
They could have gone with the characters of Candy Canady, Griff King, and Jaimie Cartwright (who was adopted by Ben and thus should have been the rightful heir to the Ponderosa). But instead, the producers brought in Ben's sea-faring brother Captain Aaron Cartwright and several of Ben Cartwright's grandchildren. One of these was Josh Cartwright, the illegitimate son of Hoss Cartwright.
Later that night a young man, who has gun in his hand, is caught by Mr. Mack. He says that his name is Josh and Hoss Cartwright is his father, and that he abandoned him and his mother, who died recently. Aaron gives him a bed for the night and the next day, he takes him to Hoss' grave and tells him that he died before he could back to get him and his mother and they didn't know where to find them.
The Cartwrights should have sued the stone-mason over that gravestone. Hoss was born in 1836 and he died in 1872. His death was even mentioned on the series at the beginning of that last season, and it was accepted that each episode aired 100 years after the story supposedly took place.
Besides, his first name of "Eric" should have been included.....
In 1871, Hoss Cartwright came to the aid of an actress who could be called "The Iron Butterfly", Lola Fairmont. While hiding out with her in the cabin of an old hermit named Grady, Hoss became attracted to Lola and eventually she returned his affections as well. How could he resist her? Not only was Lola Fairmont beautiful, but as Grady put it, "she's got a shine with the yarbs."
She proved to be an excellent cook and Grady especially liked her dry apple pie. With his enthusiastic intake of the meal (and perhaps abetted by some whiskey), Grady was soon unconscious to the world. And I think Lola took that opportunity to act upon her feelings for Hoss, who probably couldn't put up too much resistance as he had been earlier incapacitated by an iron poker to the head in an attack. No matter how badly he was injured however, apparently Hoss rose to the occasion. (Sorry about that, Chief.)
And so that's the long way around to my way of saying that I think Josh Cartwright is the son of Hoss Cartwright and Lola Fairmont.