According to the instructions of the Ministry of Taiwan Transportation, Taoyuan International Airport (TIA) or Taipei Songshan Airport (TSA) to Taipei City, the fare is charged by taxi meter (meter fare).
Please final details in the following URL: https://www.cdc.gov.tw/Category/QAPage/GIlmlkJm5EdYs81Juy8j0w
Civil Aeronautics Adminstration (MOTC R.O.C.) > transportation plan from the airport QA: https://www.caa.gov.tw/Article.aspx?a=3034&lang=1