In the Southern Song Dynasty era, Chinese sailors discover the West Coast of North America and cinnabar in the San Francisco Bay, which is associated with immortality in Chinese medicinal lore. A mining colony manned by convicts and corvee laborers with a small garrison and a Mandarin bureaucrat overseeing it is put in place near the site of OTL El Cerrito, CA. The mining colony goes on several decades, shipping cinnabar back to mainland China regularly and having varying interactions with the Ohlone and Yurok tribes around them. Kublai Khan conquers the Southern Song and the deported cinnabar miners, the garrison and the recently appointed Mandarin are left on their own, unable to return home and probably would not if they could due to fear of being killed by the Mongols.
The cinnabar mining settlement survives on its own and the stranded convict and corvee laborers, soldiers and Mandarin take native wives from the Ohlone tribe and the settlement eventually grows into a small city, with the Mandarin's descendents the ruling dynasty, calling themselves kings rather than Emperors. Their culture is Confucian with some Native mythology and traditions mixed in due to their interbreeding with the Ohlone and Yurok.
The Yuan Dynasty falls and Kublai Khan, while initially planning to seize the cinnabar mining settlement, abandons the idea after being defeated against Japan.
They survive on their own for perhaps a century. Their population grows and agricultural settlements are created to the north in the area of Sonoma, Vallejo and Benicia and another large town near the site of OTL Monterrey, CA. There are occasional wars against hostile native tribes and bandits that hide in Big Sur or the redwood forests to the north in OTL Humboldt, Del Norte and Mendocino counties. The Mandarin Kings allow Ohlone and Yurok who swear allegiance to them to serve in their armies, which many do, having little other option when epidemics of cholera, typhoid and other diseases kill off large portions of their societies.
The Ming briefly establish contact when a Treasure Fleet visits in 1408 and the current Mandarin King gives amounts of gold and cinnabar from the gold mines to the north that they have recently established and the Treasure Fleets do not return after the Ming turn inward.
The Cinnabar Kingdom as it is called, Daanguo in Chinese, becomes the dominant military power in the region and its junks go as far south as Acapulco and as far north as Pugets Sound and Vancouver, trading with the natives.
In 1542, Juan Rodriguez Cabrillo is sent north with ships after the Spanish conquest of the Aztec empire on rumors of a wealthier empire far to the northwest and a captured Daanguo Han Chinese ambassador taken prisoner in Tenochitlan.
Cabrillo sails up the California coast, and eventually encounters the Chinese and native mixed city at the site of OTL Monterrey and there is a brief but fierce battle with the soldiers of the Daanguo when Cabrillo tries to claim it for Spain and his conquistadors read the Han and Esselen residents the Rigormorento.
Cabrillo is killed in the battle as is his most of his group. The court eunuch in charge of governing the city reports back to the Mandarin King, who begins conscription to strengthen the army.
Later, Sir Francis Drake comes upon the main city of Daanguo, now larger than many European cities, with Confucian and Buddhist temples, a large palace for the Mandarin King, army citadels and a port, as well as fish markets and storehouses for gold and cinnabar mined in the vicinity.
Drake and his men are greeted with suspicion after the armed encounter with Cabrillo but allowed to dock and reprovision but after a week, are told to leave. Drake determines the settlement too well armed and defended for his crew to successfully occupy it or claim it for England, and withdraws with his ship.
Daanguo is left alone after that, aside from occasional passing British, Spanish or later on Russian trading ships from Alaska who are stopped at OTL Alcatraz Island in the Bay, allowed to trade for a week, then forced to leave.
The Spanish empire reaches to a border a few hundred miles south of Daanguo eventually, the Missions and Presidios going to the region of OTL Goleta and then a large wilderness hinterland between them, as the Spanish think the Daanguo Kingdom too difficult for them to defeat after Cabrillo and many native tribes support them or are armed by them in the area.
Mexico declares independence from Spain and these areas become part of Mexico while the United States expands inland on its program of Manifest Destiny.
US Anglo-American settlers moving west on their wagon trains find Daanguo unwelcoming but covet its vast wealth and illegal squatter settlements of American prospectors and frontiersman are established in its borders and corrupt eunuchs and Mandarin bureaucrats and Royal Army commanders let them stay without evicting them for payments.
Eventually, the US Congress determines that Daanguo presents an unacceptable obstacle to US trade and settlement, and a US Navy detachment is sent into the Bay to open Daanguo to trade.
The Mandarin King reluctantly allows US traders and prospectors in and US Naval vessels to dock in their territory under threat of bombardment from the warships docked off the East Bay.
As US settlers and merchants flood into Daanguo, a movement by the Americans for annexing Daanguo to the United States begins. Though the majority of the region is overwhelmingly Han Chinese with Native American ancestry mixed in, the US settlers are well organized and have support from the US government which covets Daanguo's natural resources, wealth and access to the Pacific Ocean through its ports.
US settlers and farmers in the Yan Province organize a revolt and march on the capital and depose the Mandarin King declaring a Pacific Republic, then petitioning the US Congress for annexation which is swiftly granted with George Donner its first and only president.
The Pacific Territory as it becomes known, comprised former Daanguo territories and most of its former population. There are several Han and native revolts that are put down by the US Army and local militias over the next decade.
The Pacific Territory applies for statehood and is granted it with restrictions on voting rights for the Chinese and natives.
Southern California, taken from Mexico in the Mexican American War is administered as the state of California while the former territories of the Daanguo Chinese kingdom are the state of Jefferson.
Present day Jefferson is a prosperous and wealthy state in the Union with a substantial tourism industry, though there are significant sentiments that the Daanguo Kingdom should be restored by the Han majority and occasional acts of political violence towards that end, as well as reports of informal hostility to Anglo-American tourists or residents of the area on a similar scale to Hawaii or Puerto Rico.