The Code of Jewish Law clearly states that a child of a Jewish mother is Jewish, regardless of the father’s lineage (or whatever else may show up in a DNA test), while the child of a non-Jewish mother is not Jewish. Matrilineal descent has been a fundamental principle of Torah since the Jewish people came into existence.
https://www.chabad.org/library/article_cdo/aid/601092/jewish/Why-Is-Jewishness-Matrilineal.htm