Presidential and Vice Presidential Election and Recall Act Article 68

In the case of vacancy of the office of the vice president, the president shall within three months nominate candidates for the by-election carried out by the Legislative Yuan.
中文原文 總統副總統選舉罷免法(新840809制定)第68條
副總統缺位時,總統應於三個月內提名候選人,由立法院補選之。

English translation for reference only; the Chinese text prevails. Not legal advice.