They also have a licensee (and early R&D investor) in China, Fosun Pharma. I don't know if Fosun is actively manufacturing and distributing, but I think they have the exclusive rights for the Chinese mainland, Hong Kong, Taiwan and Macau.
Wiki: https://en.wikipedia.org/wiki/Fosun_Pharma#COVID-19
I cannot find any references via Google that prove Fosun Pharma has exclusive rights for Taiwan. If anyone has any specifics, please reply. Honestly, I doubt it, as Fosun in a mainland Chinese corporation and China was actively blocking Taiwan out of international COVID efforts efforts vis-a-vis WHO (World Health Org).
https://investors.biontech.de/news-releases/news-release-det... (2020)
TW CDC PR: https://www.cdc.gov.tw/En/Bulletin/List/7tUXjTBf6paRvrhEl-mr...
Hence the donations
To be fair, Taiwan (Officially the Republic of China) also claims that it is a part of China and is in fact the rightful rulers of China. The Kuomintang withdrew to Taiwan after losing control of mainland China to Mao and the Communists. I'm not super up to date on the latest claims between China and Taiwan, but Taiwan has never recognized officially that they do not rightfully control China.
Latest: https://www.info.gov.hk/gia/general/202110/16/P2021101600482...
(they keep falsely claiming Baxter to be a city in Germany. It's a company that manufactures for BioNTech, not a city. https://www.baxter.com/)
<< Quality
60. Where is the Comirnaty vaccine supplied to Hong Kong produced? How to ensure the quality of vaccines supplied to Hong Kong?
According to the information provided by Fosun Pharma, the Comirnaty vaccines for Hong Kong will be produced in Germany. Click here to read the package insert.
The vaccine manufacturer must comply with the Pharmaceutical Inspection Co-operation Scheme (PIC/S) Good Manufacturing Practice (GMP) standards, or equivalent. The imported vaccine also has a Certificate of Analysis to prove that it meets the specifications. >>