Several of these links didn’t work for me for some reason, I have updated them below marked with an asterisk (Thanks @tando):
National Conscription Agency, Ministry of the Interior
https://www.nca.gov.tw/Enaspx/Default.aspx
內政部役政署
https://www.nca.gov.tw/Chaspx/Default.aspx
*Act Of Military Service System
https://law.moj.gov.tw/ENG/LawClass/LawAll.aspx?pcode=F0040001
*Enforcement Statute for Substitute Services
https://law.moj.gov.tw/ENG/LawClass/LawAll.aspx?pcode=D0040017
*Regulations for Exit of Draftees
https://law.moj.gov.tw/ENG/LawClass/LawAll.aspx?pcode=D0040006
*Punishment Act for Violation to Military Service System
https://law.moj.gov.tw/ENG/LawClass/LawAll.aspx?pcode=F0120002
*Conscription Regulations for Naturalized Aliens and Returning Overseas Chinese
https://law.moj.gov.tw/ENG/LawClass/LawAll.aspx?pcode=D0040005
*尚未履行兵役義務男子申辦護照及僑居身分加簽限制辦法
https://law.moj.gov.tw/LawClass/LawAll.aspx?pcode=E0030015
*常備役體位因家庭因素及替代役體位服補充兵役辦法 (“alternate” (shorter) service 12 days a conscript)
https://law.moj.gov.tw/LawClass/LawAll.aspx?pcode=D0040023
國家體育競技代表隊服補充兵役辦法 (“alternate” (shorter) service for athletes I think)
https://law.moj.gov.tw/LawClass/LawAll.aspx?pcode=F0040025
國際組織技能競賽國家代表隊服補充兵役辦法 (“alternate” (shorter) service for people with “skills” I think)
https://law.moj.gov.tw/LawClass/LawAll.aspx?pcode=N0080049