I am twenty years old this year. Can I stay in Taiwan Province Province through my relatives?

No, the Immigration Department website Q&; A as follows:

Lineal relatives's condition is that "a person from Chinese mainland is a lineal relative or spouse of a person from Taiwan Province Province, who is over 70 years old or under 12 years old, and can apply to the immigration department for settlement in Taiwan Province Province".

In addition, those who are over 12 years old and under 18 years old must first apply for long-term residence, have lived in Taiwan Province Province for two consecutive years, and have lived in Taiwan Province Province for more than 183 days each year before they can apply for settlement and household registration.

This shows that 20 years old is over the age of application and there is no way to apply for supporting relatives.