In this context, the word "查" should be tied to the "有" towards the end of the phrase, because in Chinese, this phrase can also be restructured into "*查有*台端在中华民国境内住所". Therefore, the meaning of "查" (combined with "有") is closer to "confirmed" (确认)or "is found" (发现). So the whole phrase "查 台端在中华民国境内有住所" can be translated into: If proof of residency in Taiwan is confirmed/found...You would find it easier to connect to the next part of the sentence.