Jews from gentile fathers- were they always considered Jews?

Despite Talmudic passages claiming a person born to a Jewish mother and a non-Jewish father is "100% Jewish" I have heard that there was a period of Jewish history, over 1500 years prior to 1901, where nobody was recognized as being born Jewish if they had only one Jewish parent. In that period, if a Jew intermarried they converted to other spouses religion first, and no child from the union would have been considered Jewish is the main reason for this. Can you name any person born Jewish with a non-Jewish father in the 401-1900 period? I haven’t found any.

I don’t know what your source is, but it’s not an accurate rabbinical or knowledgeable source. For example the Pitchei Tshuva on Even HaEzer 4, which was written in the 19th century, and he quotes poskim from the 18th century, who discuss unfortunate cases where the father wasn’t Jewish, yet the halacha relates to the child as totally Jewish. As in all such responsa, the name of the child involved isn’t mentioned for obvious reasons, including the sake of privacy. It’s true that you won’t find too many mentioned because in fact, even though the child is halachically Jewish, the union of the mother with a non-Jewish man almost always stemmed from her desire or willingness to leave the Jewish people, or if the mother was raped by a gentile, she wouldn’t publicize the issue.