https://en.wikipedia.org/wiki/Matrilineality_in_Judaism
The Hellenistic Jewish philosopher, Philo of Alexandria (c. 20 BCE – 50 CE) calls the child of a Jew and a non-Jew a nothos (bastard), regardless of whether the non-Jewish parent is the father or the mother. Flavius Josephus (c. 37-100 CE), the Romanized Jewish historian, writing about events that were alleged to have occurred a century prior, has Antigonus II Mattathias (c. 63-37 BCE), the last Hasmonean king of Judea, denigrating Herod –whose father's family were Idumean Arabs forcibly converted to Judaism by John Hyrcanus (c. 134-104 BCE) and whose mother, according to Josephus, was either an Idumean Arab or Arabian (Nabatean-Arab)– by referring to him as "an Idumean i.e. a half-Jew" and as therefore unfit to be given governorship of Judea by the Romans:
But Antigonus, by way of reply to what Herod had caused to be proclaimed, and this before the Romans…said that they [the Romans] would not do justly, if they gave the kingdom to Herod, who was no more than a private man, and an Idumean, i.e. a half Jew, whereas they ought to bestow it on one of the royal family, as their custom was; for that in case they at present bear an ill-will to him [to Antigonus], and had resolved to deprive him of the kingdom, as having received it from the Parthians, yet were there many others of his family [the Hasmoneans] that might by their law take it, and these such as had no way offended the Romans; and being of the sacerdotal family [the Hasmoneans], it would be an unworthy thing to put them by.