Which one is correct:
- на материковом Китае or
- в материковом Китае
- на континентальном Китае or
- в континентальном Китае
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Choice of adjective. Both "материковый Китай" and "континентальный Китай" are widely used, sometimes in the same document. However, the Lingvo dictionary gives only one translation for "mainland China", and it is "континентальный Китай". May be that the dictionary needs expansion, may be that "континентальный Китай" is the official term.
Choice of preposition. It is a part of China, and according to the rules of preposition selection, it should be "в", just as "в Китае", which is a country and not an island. Another example which may be less confusing is "континентальная Европа" and "в континентальной Европе". However, strictly speaking, it is a different part of the rule, because Europe is not a country.
At the same time, I can't help mentioning that examples with preposition "на" are also widespread. That being said, standard is "в", but both forms are possible in colloquial speech.
The choice of the preposition
на/в is paradigmatic, but with multiple exceptions.
на is used for the following regions:
Named after the islands: на Кубе, на Ямайке, на Гаити, на Фиджи (but в Гренландии, в Исландии, в Британии). Сompare to на остров.
Lake and river basins: на Валдае, на Байкале, на Волге. Сompare на реку, на озеро.
Mountain ranges in singular: на Урале, на Кавказе, на Памире (but в Альпах, в Гималаях, since they are in plural, в Тянь-Шане). Compare to на гору, but в горах.
Ending in -чина, -щина: на Брянщине, на Новгородчине.
This is by far not a complete list and it's always best to consult the dictionary in each case.