OK - I see. I can't read Chinese, but I now see at the bottom of the page there's nothing for iPhone or Apple Watch like there is on the US AppleCare page.
AppleCare - Apple
So no. Apple apparently doesn't offer AppleCare or AppleCare+ for iPhones in Taiwan. Also - AppleCare/AppleCare+/warranties for iPhones don't transfer internationally, so buying one where AppleCare is offered wouldn't help. You might be able to find a company that offers some sort of extended service contract, but it may be tied to a network of aftermarket repair businesses, and that may result in Apple refusing to service (even a battery replacement) a device that they consider to have been tampered by an unauthorized repair facility.
Still - you might not get Apple's phone service beyond the one year warranty, but isn't there an Apple Store at Taipei 101? If you can show up in person, Apple Store service is the best I've ever seen. They don't charge a thing to diagnose a problem, and a lot of the fixes can even be free as a courtesy if there's no actual physical repair that requires parts. Just yesterday I was at one trying to diagnose my iPad Mini 4 WiFi issues. I was there with my child and after checking in. I waited next to my child (playing a game on a Mac) while waiting to be called when the Apple employee came to me. The entire diagnosis was done right there rather than being told to go to the "Genius Bar". On top of that, I bought my device at an authorized reseller (at an extremely good sale price) and not an Apple Store. That made no difference to Apple in how I was treated. When you pay a premium for an Apple product in an area with Apple Stores, you're getting that level of support no matter where you bought the device.
Now if you're in Kaohsiung then you can ignore all that praise about Apple Store service. 😉