Some students probably get an extra subsidy from your department or advisor for some research project.
According to the Bureau of employment, before the labor relationship happens, the student must apply for work permit.
Thus, please remember to apply for the work permit. Before application, please read the regulations and the rules attached to the application form.
Foreign graduate student of the first year may apply for it but under certain conditions regulated by the Regulations on the Permission and Administration of the Employment of Foreign Workers.
Students can apply for a work permit at each beginning of the semester (but you are allowed to apply anytime) however, it should be before the labor relationship happens.
Note: Working without a permit carries a fine of up to NT$150,000