The Mishna, Bikkurim 1:4, speaks of converts to Judaism who bring their first fruits to the temple, or who pray within a synagogue:
אלו מביאין ולא קורין הגר מביא ואינו קורא שאינו יכול לומר אשר נשבע ה' לאבותינו לתת לנו ואם היתה אמו מישראל מביא וקורא וכשהוא מתפלל בינו לבין עצמו אומר אלהי אבות ישראל וכשהוא בבית הכנסת אומר אלהי אבותיכם ואם היתה אמו מישראל אומר אלהי אבותינו
The following people bring [the first fruits] but do not recite [the accompanying declaration]. A convert brings but does not recite, since he cannot say "[I have come to the land] that the Lord swore to my ancestors to give us" (Deuteronomy 26:3) - but if his mother is Jewish, he brings and recites.
When he prays to himself [ie: silently], he says "God of the ancestors of Israel" [instead of "God of our ancestors"], but if he is in a synagogue he says "God of your ancestors". And if his mother is Jewish, he says "God of our ancestors".
Given that this person is a convert, it stands to reason that prior to his conversion he was a gentile. How am I to understand the mishna's reference to a convert whose mother is Jewish?