Answered by ZUPAN
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Oct. 29, 2019 10:32
Both legs of your itinerary are definitely eligible for 24 hour visa free transit and you don't need any kind of visa.
You will print out your flight tickets and have the printouts with you. Also, you will declare in Taipei that you will travel to Los Angeles via Xiamen using 24 hour visa free transit. You will do the same thing in Los Angeles where you will declare that you will travel to Taipei via Xiamen using 24 hour visa free transit.
Just be relaxed because you are perfectly eligible and don't listen to unsubstantiated rumors from the people that really cannot read the very basics of Chinese visa free transit policy.