"According to [early] Roman law, a child is the legal heir of his father and is in his father's custody (potestas) only if his father and mother were joined in a legal marriage (justum matrimonium). The capacity to contract a legal marriage was called conubium (or ius conubii), and was possessed almost exclusively by Roman citizens. Marriage between a person with conubium and a person without conubium was valid, but it was not a justum matrimonium; and without a justum matrimonium, the status of the child follows that of the mother." - Shaye J. D. Cohen, "The Beginnings of Jewishness," page 294.
According to Jewish law, a child follows the tribal status of his father if both his father and mother possessed the capacity to join in a legal marriage. This capacity is called kiddushin and is possessed exclusively by Jews. Relations between a person capable of kiddushin and a person incapable of kiddushin, say a Jew and a Gentile, results in the status of the child following that of the mother.
An echo of Roman law in Halachic matrilineal descent?