I checked many Taiwanese and the US government websites and I didn't find a specific official list of accredited schools in the US that is also recognized by Taiwanese Ministry of Education.
MOE in Taiwan does have a list showing accredited traditional universities (not online universities), but it is just a reference (as a suggested guide) for Taiwanese students who are looking for studying abroad and get a degree abroad. It is not a final official document with government authority. Plus, it was last updated in 2005. If you think of that most online universities start in recent years, you'll realize online universities and colleges are not going to be listed on that document. The document also has a note saying that all schools listed there are just for reference. The diploma from individual school still needs to be sent to relevant government office for review and approval.
On Taiwanese MOE website, it writes that students should check with the US department of education (I've put the link on the bottom) to make sure the school you are choosing is accredited by a reliable accrediting agency. (I've listed an online college and university directory on the bottom, which only lists accredited online schools.) I am guessing this probably means that Taiwanese MOE accepts the degree from schools which the US department of education recognized. As long as the school is really accredited in the US standard, it should be okay with Taiwanese MOE.
So, you should check the website of the US department of education by yourself (not rely on other agencies that help you to apply schools abroad) and double check with the Taiwanese Bureau of International Cultural and Education Relations to make sure that online diploma you are getting is useful in Taiwan.
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