Government site explains most things you need to know. I link some relevant instructions from the website of National Immigration Agency of Taiwan below.
you should reside in Taiwan for a while to get a citizenship.
In the case you can get a residency,
- Get your TARC (Taiwan Aria Resident Certificate).
- Continuously reside in Taiwan for a certain period on the TARC. The minimum is 1 year with no exit.
If you cannot get a residency,
- Get an entry and exit permit. you can stay in Taiwan for 90 days and apply for another 90-day extension once each time.
- Repeat visa runs, and continuously stay in Taiwan for more than 183 days each year for 7 years.
- Then, you are now eligible to get a TARC.
Short-term residency of nationals without registered household in Taiwan area
https://www.immigration.gov.tw/5475/5478/141465/141808/141985/
TARC
you should have some eligibility listed in the following page.
Notices for the Application of National Living Abroad without Registered Household in Taiwan Area for Residence in Taiwan Area
https://www.immigration.gov.tw/5475/5478/141465/141808/141954/
How to get a citizenship.
Notices for the Application of National without Registered Permanent Household in Taiwan Area for Residence after Continuous residence or residence for certain period of time
https://www.immigration.gov.tw/5475/5478/141465/141808/141950/