According to Articles 31, 74-1, and 18 of the Immigration Act, foreign nationals who need to continue their stay or residence after the expiration of their permitted stay or residence period must apply for an extension with the National Immigration Agency (NIA). Overstaying will result in a fine ranging from NT$10,000 to NT$50,000 and a re-entry ban of at least one year and up to seven years.

During your stay in Taiwan, if you need to continue your stay or residence for academic reasons, you must apply for an extension with the NIA:
(1) For those holding a visitor visa, you must apply in person at any NIA service center within 15 days before your permitted stay expires.
(2) For those holding an Alien Resident Certificate (ARC), you must apply through the "Online Application System for Foreign and Overseas Students" within three months before the expiration of your residence period.

For more detailed information, please refer to the guidelines on the NIA's official website: https://www.immigration.gov.tw.