A Taiwan visa cannot be obtained by citizens of the People's Republic of China, Hong Kong, or Macau. They must get an Entry and Exit Permit instead.
If any of the following apply to them, nationals of Hong Kong and Macau must get an Entry and Exit Permit:
passport for the Hong Kong Special Administrative Region (HKSAR)
British National Passport (Overseas) (BN(O)
passport for the Macao Special Administrative Region (MSAR)
You can apply for a Taiwan Entry and Exit Permit online if it's your first time receiving one. Once you've used the Permit to enter Taiwan once, you may get it using an easier process online or when you get there.
You no longer need to hold an entry and exit permit if you are from Hong Kong or Macau but have acquired citizenship in another nation. You must abide by the laws of the nation in which you now reside.
Mainland Resident Travel Permits, which are available from Chinese authorities, are required for citizens of the People's Republic of China to travel. They also require an Entry and Exit Permit, which they can only get if they are travelling in a group that has been approved in advance.