You can apply for a part-time work permit if you have studied Chinese for one year in Taiwan and hold a residence permit. The working time is up to 20 hours per week except winter and summer vacation. You cannot work part-time without a work permit. Apply for a work visa website https://ezwp.wda.gov.tw/wcfonline/wSite/Control?function=IndexPage

Legal reference for foreigners working in Taiwan : 

https://law.moj.gov.tw/LawClass/LawAll.aspx?pcode=N0090027

※ Those who fail to comply with the above regulations may be subject to relevant penalties and fines as follows:

1. In accordance with Article 50, Item 1 of the Employment Service Law, and the Employer’s Approval and Management Measures for Employing Foreigners, foreign students must first apply for and obtain a personal work permit to work in Taiwan. If they do not apply for and obtain a work permit in accordance with the regulations If you are employed to work for others, you will be fined NT$30,000 to NT$150,000, and if you employ a foreigner who has not legally applied for a work permit, you will be fined NT$150,000 to NT$750,000. Penalty. For application materials and procedures, please contact the Workforce Development Agency of the Ministry of Labor (Tel: 8995-6000).

2. If the employer wants to hire a foreign student, must check the original of the student's residence permit, student card and work permit, and check the basic information on the certificate, residence time, reason for residence, and work permit period (the maximum period of the permit is 6 months ), and take photos to keep as evidence. In addition, it should be noted that the working hours of foreign students are up to 20 hours per week except for winter and summer vacations.