Answered by Borut | May. 24, 2023 15:41
There is no problem with Taiwan because it is considered as eligible territory, but the problem is that your itinerary:
Taiwan - Beijing - Taiwan
Is just a return trip and not a transit. You need your immediate points before and after Beijing in different countries or different territories. For example, something like this:
NYC - Taiwan - Hong Kong - Beijing - Taiwan - NYC
As you can see, immediate points before and after Beijing are in two different territories and this makes you a transit passenger and consequently eligible for 144 hour visa free transit.