Hesperia is the name OTL America got.
Northern Hesperia: Erik the Red's son, Leif Eriksson, explores the shores of Helluland (*OTL Baffin island), Markland (*OTL Labrador) and Vinlandria (*OTL Newfoundland); he settles in this last island, where he meets the native and has pitched skirmishes with them, then comes back to Greenland with interesting news but little to show.
The Icelander Thorfinn Karlsefni leads a Norse settlement at Vinlandria: Thorfinnsvìk (*not existing OTL, some 50 kms due west of OTL St.Anthony) is the first European hamlet in the New World.
The distances and the hostility of the natives force the few Norsemen in Vinlandria (*OTL Newfoundland) to sail back to Greenland; Thorfinn Karlsefni immediately sets sail to Iceland, and thence to Norway, where he gathers some hundred colonists (mainly people fleeing Danish rule) who, after an epic cruise, re-establish the colony at Thorfinnsvìk on the Hesperian (*American) island.
Vinlandria's few natives are almost completely exterminated by the unknown diseases brought there by the Norse settlers, whom they vainly fought off. Tales of “golden-headed giants” leak on the Hesperian continent together with the new, unknown illnesses which will reduce the natives of northeastern Hesperia by a half in a few decades before a minimum immunization is reached.
A second wave of Norse settlers led by Ragnar Arnarsson reaches Vinlandria from Greenland. By this time the European community on the island reaches about 1000 people; the new influx of settlers makes Christians the majority of Hesperian Norsemen.
The Norsemen of Vinlandria explore the coasts of northern Hesperia from Helluland Sound (*OTL Baffin Bay) up to New Palestine (*OTL Massachusetts); the extent of their discoveries, though, goes completely unnoticed in Europe, where it feebly echoes as a Scandinavian saga no more credible than those on sea monsters of trolls.
A tiny Norse colony established in what will be later called New Palestine is overwhelmed and destroyed by the local Skraelings.
A third wave of Norse colonists from Norway, Iceland and Greenland reaches Vinlandria, where by now some 1,500 Europeans live in several settlements in the north of the island on fishing, timber and petty trades with the Skraelings.
A last influx of Norsemen from Iceland reaches Greenland.
The Iceland-born Thorstein Sigurdsson the One-Eyed, with some dozens of companions from Vinlandria, establishes a stable Norse colony at Thorsteinsflo (*OTL Dingwall bay) in Marksey (*OTL Cape Breton island). They soon enter into contact, and sometimes conflict, with the local Mikkmakk natives
The Rauthljudar (Red Screamers, *OTL Beothuks) natives of Vinlandria, much reduced in numbers by European-imported illnesses, are unified under the leadership of the mixed-blood half-Norse Leif Strong-Axe, who enforces Christianization upon them and asks for a bishop from Iceland or Scandinavia
The Norse bishop Eirik leads a party of Vinlandrians, both Norsemen and Red Screamers to found the first successful European settlement on the Hesperian mainland, Eiriksnes (*on OTL Cape George Point) in Skraelingarland (*OTL Acadia).
Bishop Eirik of Vinlandria is killed while trying to convert (Gospel in the hand, battleaxe in the other...) the native Mikkmakks of Skraelingarland. He will be later sanctified and made into St. Erik, Protomartyr of the Hesperias.
The native peoples of NE northern Hesperia are halved in numbers by fierce epidemics brought in by Norse and Red Screamers colonists and tradesmen from Vinlandria and Skraelingarland. Some of the native Maliseeths, Abenakis and Mikkmakks absorb the tenets of Christianity together with crypto-pagan Norse customs. Writing is introduced among the natives through rune-carving, and rapidly adapted to their Algonquian languages; the use of iron and metals also spreads.
A handful of Hesperian natives, captured by Icelandic traders, end up in Lübeck, where they are referred to as “Indians” and soon die of European diseases.
The Norseman Olaf Eiriksson explores the southern fringes of Skraelingarland, that is the lands later to be known as New Palestine (*OTL Massachussetts, New Hampshire and Maine).
The Welshman Riryd, exiled by his brother earl Madoc of Dublin, sails northwest with a hundred Welsh and Irish followers, touching Iceland and Greenland and ending his voyage in Vinlandria, a land he heard of through the dim hints of Icelandic tradesmen in Ireland. There he meets the Hesperian Norsemen and leads their first exploration of Bakkland (*Québec and Ontario) and the Great Lakes. As most Norsemen turn back on the long and dangerous route, Riryd with his followers continues by canoe and on foot, exploring the lands due south of the Great Lakes, where a native kingdom exists, centered in OTL Cahokia. Riryd and his men, at first welcomed as demi-gods, are soon chased out as fierce epidemics ravage the land, and take refuge further south among an Hesperian nation, the Rwadhas (*OTL Mandans), mixing with them. Their adventure will be preserved through oral tradition, and only later their lot will be known through the northeastern Hesperian peoples, who are by now gaining a grasp on rune-carving from the Norsemen.
The Rwadhan culture arises between OTL central Appalachians and OTL Mississippi river: the natives, after learning from Riryd's Welshmen metal-working and the use of the longbow, soon are able to dominate vast swaths of sparsely populated land.
The Norsemen of Skraelingarland, thanks to an otherwise unnoticed ship coming from Iceland, introduce the first horses in Hesperia, mostly to their very surprise since even they hadn't had any for some two centuries. Against the encroachments of the Norsemen, now organized into a vaguely theocratic league under a bishop and a Lawspeaker, with half-blood and natives as thralls (serfs), and their allied tribes the first strong Mikkmak kingdom arises, led by a succession of rulers known with the Norse name of Banskeknungar.