In the year 1381, the Danish prince Harald went on a journey with some fishermen, interested in their tales of lands in the west. They landed in OTL Newfoundland (named Prince-Haralds-Land, eventually shortened to Haraldsland), meeting some Indians. Prince Harald claimed the land in the name of the Danish king, returned to Europe together with some Indians, presenting them to the astonished courts of Europe.
In 1387, he started his second journey to the New World. This time, he came as far as OTL Manhattan Island, which was named Prince-Harald-Island. In the following years, several other ships would go to the New World, return with plants and animals. After the first curiosity had ebbed, people in Europe mostly didn't care about the new lands any more, though. A few fishermen made settlement on Prince-Haralds-Land, Cape Cod and Manhattan Island, but that was all for the moment.
1435, Black Death hit the New World, destroying some small European settlements too; other trade places had to be given up, since the Atlantean trade partners had died or didn't want to have contact with the Europeans any more. They now concentrated on a few places: Haraldsland, New Jutland (Nova Scotia), Prince-Harald-Island, Nieuw Zeeland (Atlantic City island), plus the Scottish-Norwegian colony on Martha's Vineyard.
After the separation of their countries, the kings of Denmark and the Netherlands finally agreed in 1438 for a compromise in the New World, which was negotiated by the pope: Denmark kept the northern colonies (Prince-Harald-Island, Haraldsland, New Jutland), which were extended with time over the whole OTL Canadian Maritimes and the Hudson valley. The Netherlands got the Southern colony of Nieuw Zeeland and were allowed to colonize the lands further South.
After some clashes with Danish colonists in Atlantis, the Quadruple Monarchy declared the anti-Danish War (1509-12) against Denmark. The Dutch allied with the former. In the peace of Hamburg, Denmark lost its lands in Canada to the Quadruple Monarchy and Anderland to the Netherlands. Only the city of Haraldsborg (OTL New York, plus Long Island) and Prince-Haralds-Land (as a base for fishermen) stayed in their hands. And even worse, in 1544 in Haraldsborg chaos ensued after the mother country fell into civil war. Now Poland sent soldiers to the city, occupying it. Haraldsborg became the portal for Polish and Prussian immigrants to (Northern) Atlantis.
When king Alasdair IV was elected Polish king, he controlled Haraldsborg again, helping to calm down the relations of Danes and Poles in the city. His reign stayed a short episode, however; and in the English-Polish War 1613/14, Poland lost OTL Trinidad and Haraldsborg to England, making the city a part of New England.
In 1637, however, the Dissenter's Revolt happened in New England. Denmark-Braunschweig, supported by France, used the situation to expand there / take old lands back. Only Markland (OTL Canadian Maritimes and Quebec) could defend itself during this decade, ironically, thanks to its strong garrison. Denmark-Braunschweig got Haraldsborg back, plus became protector of the Commonwealth of New England (the dissenters preferred "the papist German king in Europe to the papist English governor in Markland"). German immigration now also went to New England, where many new settlements were founded. English loyalists emigrated to Markland. In 1642, the colonies of Denmark-Braunschweig (Martinsburg, Waldstätten, Nieuw-Nederland, Haraldsborg and Anderland) were united under a common administration.