In the late 9th and early 10th century AD, Scandinavians under the leadership of Leif Eriksson managed to reach the northeast coast of North America. They called various regions of the northeast Helluland, Markland and Vinland, traded with the natives and established a small seasonal settlement on the coast, for logging timber, and replenishing supplies of food (fish, foraged berries) and water. Though long-suspected to have possibly occured, based on some Norse sagas, it took until 1960 for archaeologists to find the location of the seasonal settlement briefly inhabited by Eriksson and his followers, at today's L'Ans aux Meadows in Atlantic Canada. Ever since then, it's become common knowledge that the first Europeans to reach the New World were the Scandinavians around 1000 AD, though they didn't intend to establish a permanent home there.
To no one's surprise, the confirmation that the Scandinavians did reach North America was a major boon for fans of the burgeoning genre of alternate history fiction. With the genre's growing popularity since the 1990s, the idea of the Scandinavians establishing a long-term colony in North America took a foothold in the imagination of many. Vinland colony scenarios were appearing already in the early days of the genre's Internet fandom, in various discussions and early online-published stories. They remain a popular speculative medieval scenario to this very day.
At one end of the spectrum, you have Vinland-themed timelines that really try to pay attention to historical plausibility, realistic motivations of Scandinavian settlers and their potential drawbacks, the role of the native cultures in the narrative, the resource and logistics issues with colonizing the coast of North America from the other side of the Atlantic with 11th century technology, and so on and so forth. Though the results vary, these sorts of stabs at the idea of a “Vinland colony” and an at least smaller or semi-assimilated North American viking settler culture often prove intriguing.
At the bad end of the spectrum, you have badly written alternate histories with sloppy research, that are often little more than “viking superiority” porn. These tend to disregard the Native American peoples role in such an alternate timeline completely or treat them as a nuissance to be overcome, rather than bothering with a nuanced look at both transatlantic cultures, their realistic limitations, and how they could realistically influence each other.
There's also a similarly annoying but more widespread sub-cliché of this, when someone on AH.com and eslewhere asks whether Native Americans could have discovered this or that simple technology, many people immediately leap in to claim that “all they need to is have the vikings bring them that technology”. This assumes the Scandinavians were some amazing treasure trove of medieval European technology, or that they somehow even had medieval technologies centuries ahead not only of Native Americans, but even fellow Europeans. In reality, as technologically skillful and rather well-equipped as they were, the vikings weren't vastly ahead technologically even compared to New World native cultures, and they were disadvantaged even compared to other early medieval European cultures. Due to plentiful OTL evidence that the Scandinavians visiting North America weren't very willing to trade weapons and tools with the natives, and even treated many of the natives arrogantly and badly, the idea of an easy tech exchange supplied by Scandinavians is highly naive and ignores the limitations and realities on the ground.
A further misconception, in no small part fueled by pseudohistorians and supremacists ever since the early 1900s (decades before viking visitors in America were confirmed), was the notion that the vikings established a huge and developed colony in North America (or even elsewhere in the Americas). This misconception and starting assumption often crops up in some Vinland timelines, especially those of alternate history newbies who don't bother with deeper historical research before beginning writing, and severely overestimate the OTL extent of the Scandinavians' stay and activities in North America. One or at most two temporary, seasonal hamlets, that were promptly abandoned once the visitors permanently returned home, is hardly a basis for a huge, thriving colony with thousands of people. There's a degree of “computer game thinking” in accepting a misconception like this without second thought, because two or three boats of Scandinavians who arrive at the coast of North America does not mean the place will be its own Norse-speaking polity in fifty years time. Especially colonies, especially transatlantic ones without Renaissance era technological advances, is a lot tougher than many think.
The Canadian Beardmore swords hoax from the 1930s is an infamous example of pseudohistorical claims fueling misconceptions about vikings and Vinland. Said Canadian hoax involved a well-connected archaeologist with a politicized interest in “proving” the vikings had settled Canada far more than anyone expected, had real early medieval swords imported from a collector in Norway to Ontario, and then “found them” at a made-up digsite. These pseudohistorical claims even appear as recently as in the contemporary US, where a small group of viking hype fruitcakes in Minnesota (a place with many people of Scandinavian immigrant origin) created a series of hoaxes (and even a whole “museum” to house them) that supposedly “prove” vikings made it all the way to Minnesota. All these flimsily documented hoax “finds” are in stark contrast to actual archaeological proof for such a claim, which remains zero even in 2020. The fact that all these hoaxes tend to have a racist undertone of “this proves our ancestors were always here and the Native Americans don't belong here” is just icing on the cake of awful. In September 2021, the long-suspect “Vinland Map” was proven to be a complete forgery made between the 1920s and 1950s, based on modern chemical and spectroskopic analysis. The map also has several obvious anachronistic features.
What if the Vikings Introduced Europe to the New World 500 Years Earlier? - Mitro's detailed video essay on the subject, at his The Alternate Historian channel. Worth a watch.
Since the early days of online alternate history fiction, including since the founding of AH.com, there have been plenty of alternate histories that explored the idea of a long-term and surviving Vinland colony, and its impact on world historical developments. Here's a list of some of the projects, on AH.com and outside of it, that have tackled this subject matter with varying degrees of believability.