I assume your question is: Since People's Republic of China (PRC) exists, was Taiwan considered as part of it?
It is more like a political question than historical, since the current situation of PRC and ROC (Republic of China) is still unsettled since the end of the civil war.
I am sure most of us know that People's Republic of China claims Taiwan, but it is de-facto independent country. So in a way Taiwan is part of PRC.
Importantly on the other hand maybe less people know that ROC renounced in 1992 the conquest of PRC-controlled territories as a national goal, there is still dispute over whether the constitution still gives legal support to a claim of sovereignty over all of China's pre-1949 territories, including Outer Mongolia and the entirety of the present PRC. From Wikipedia
So in a way PRC's territory belongs to ROC as well.
Objectively, these two territories function as separate countries. Separate governments, currency, foreign relations.
Taiwan's independence is recognized by various countries, and most of countries have unofficial relationship with Taiwan (without embassy), but there are couple of countries have completely official foreign relationship with Taiwan including embassy.
Taiwan's de-facto independence is reinforced by USA through Taiwan Relations Act accepted in 28th February 1979.
So the answer is "yes and no in the same time", entirely depends on political view.