Here's a few ideas:
Dutch Taiwan: After the Qing reclaim the island in 1683, they go with their original plan of abandoning the island because they find it difficult to defend. However, to make some money, they sell the island back over to the Dutch. The Dutch would keep on trying to colonize the island while also supporting the secret Chinese settlements into the island. It'd likely go over under direct Dutch control. The Dutch would keep trying over to send more and more Dutch settlers into the island while directly overseen by them rather than the VOC. They'd likely be focused on stabilizing the island and over time, the Chinese and Dutch settlers would mix with one another along with the Taiwanese indigenous folk. It would be a similar phenomena to what happened with the Indo people of Indonesia. I could also see the island being perhaps used as a penal colony, especially for Belgian rebels or other potential troublemakers and the like. The connection to the Dutch and European influence would lead to growing more distinct from Qing China, which may affect China itself. especially with a potential brain drain. Beyond that, this Eurasian Taiwan would likely be granted independence after a WW2 scenario. Culture would be a mix of Dutch protestant beliefs along with the Chinese folk faiths and that of Taiwanese indigenous. It would likely be more stable and financially well-off than Indonesia and would have an odd relationship with China. What happens depends on who is in charge of China. Nationalists would probably be okay, and the Communists would cause some tension. Nation would also be an oddity for the mixing of cultures and maintaining links to European and Chinese culture while building a distinct brand of it.
British Taiwan: During the First Opium War of the 1830s and 1840s, the British manage to go and take Taiwan over from Chinese control. To go and aggressively settle the island, they go and follow similar practices that they did with Australia. I also suspect that some Irish folk may end up there as well for one reason or another. Due to the British not having that much of a firm grasp over, the mixing may still occur, if at a slower rate. Regardless, it happens and the British keep using the island as a dumping ground for the poor and unwanted. A distinct Anglo-Sinic culture is formed from this. Whoever is in charge after the Qing are gonna want the island back. If the Nationalists are in charge, it's gonna be a pretty big tense point throughout the 20th century and beyond and same with the Communists. The island would also become invested in by European and American companies and defense.
The Christian Horde: The Mongol Golden Horde would end up embracing Eastern Orthodox Christianity instead of Islam. Additionally, while the eastern part of the nation would become Turkicized, the western part of the Golden Horde would become more influenced by the Slavic peoples there. A distinct identity would be formed when the Golden Horde would break apart, with this Slavic/Mongol Horde taking the place of OTL Astrakhan Khanate in terms of location along with parts of Crimea. Because of their Chrisitian connections, they may show some favortism over to the Principality of Theodoro. The nation may end up growing to be a subordinate of Russia, not unlike its "half-sibling" Ukraine. Its Christian connections along with border to the Black Sea will have it maintain some inteest for the Christian world, epecially since their connection in trade would make it important and perhaps become inspired by the Cossacks or the like in how they do their business. They may try and revolt during the Russian Revolution.