One great Adam Cartwright fanfiction is 'The New Beginning for Adam'. It beautifully portrays his character development in a new and exciting scenario. The story has a great balance of adventure and the emotional depth of Adam's personality.
A Cartwright fanfic is basically a piece of fan - made literature. It's often a way for fans to show their love for the character Cartwright. It can vary greatly in terms of plot. Some Cartwright fanfics might be comical, with Cartwright getting into all sorts of silly situations. Others could be more serious and deal with heavy themes such as loss or redemption. The beauty of fanfic is that it allows fans to take the basic elements of Cartwright and create their own unique interpretations and stories.
I don't have enough information to say for sure. It could be fiction, or it could have roots in reality that have been adapted or exaggerated for a particular purpose.
If Cartwright Heeramandi is a relatively unknown or local story, it could be that it hasn't been widely publicized. Maybe it's a family - related story in a particular neighborhood. It could be about a business started by Cartwright in Heeramandi, or perhaps a historical event that only the local elders are familiar with.
The show 'Bonanza' was designed to appeal to a wide audience, and at that time, gay storylines were not considered mainstream. Producers likely focused on more familiar family - and heterosexual - relationship themes to attract viewers. Little Joe Cartwright's character was crafted within this framework, so there were no gay stories associated with him.
You can try searching on fanfic websites. Some popular ones like Archive of Our Own (AO3) or FanFiction.net might have Cartwright fanfic. Just use the search bar on those sites and type in 'Cartwright' and see what comes up.