Sir/mam, just want to ask, if you are a taiwan passport holder and a phillipine immigrant

If you don't have Filipino passport, you still need to use your Taiwan passport to enter HK. If you have Mainland Travel Permit for Taiwan Residents, you can use it to enter HK and stay for 7 days. You'd better bring the permit and your passport together in case they check them both.

If you don't have the permit or plan to stay longer than 7 days, you should apply for entry permit from the appointed airlines, China Airlines, for example.