You need to understand the difference between ROC nationals without household registration and nationals with household registration. Do some google search. The latter means taiwanese with full citizenship.
Where were you born? If in Taiwan, you can get a full taiwanese citizenship directly.
If not, what you can get now is an overseas taiwanese passport without identification number, which just shows at least one of your parents are with a Taiwanese citizenship when you were born. To get a full passport you can use abroad, you need to live in Taiwan for a certain period.
The following thread and other threads in this forum may help.