Vayishlach, Breishis 34:2. Matrilineal Descent.

Shechem assaulted Dinah, the daughter of Yaakov.  Chazal tell us that this episode resulted in the birth of a daughter, Asnas, who was adopted by Potiphar (and, as in the case of Moshe Rabbeinu, her adoptive family gave her this Egyptian name).  Asnas ultimately married Yosef.

Coincidentally, I saw a remarkable idea this week.  We are all familiar with the rule of matrilineal descent (Kiddushin 68b and Yerushalmi Kiddusin 3:12 and Bamidbar Rabba 19:3), that Jewish identity descends through the Jewish mother.  If a non-Jewish man fathers a child with a Jewish woman, the child is Jewish.  (This was not necessarily true prior to Sinai- see Ramban Vayikra 24:10- but that is not the topic of this discussion.)

There might be two major exceptions, or caveats, involving this rule.  They are minority opinions: neither is widely accepted.

1.  The Mahrshal in Yevamot 16b and the Maharit Algazi in Bechoros 47a (I saw it brought down as being on 56a, and I can't go look now).  They hold that such a child is only Jewish if he/she was raised as a Jew, i.e., that he/she conducted him/herself as a Jew.  Once the Jewish identity vests, it is, of course, permanent.

Maharit:

ונ"מ מזה דמאי דאמרינן דלמ"ד כשר אפילו קודם שנתגייר כשר, היינו בגוי שבא על בת ישראל בדרך זנות ונתעברה ממנו ושוב לא ידע הגוי מהולד כלל, ואמו גדלו בתורה ובמצות כבן ישראל ממש, דבכה"ג אמרינן דאיגלאי מילתא למפרע דהורתו ולידתו בקדושה ומתחלתו ישראל גמור היה ולא כגוי שנתגייר, אך אם היה הענין שהגוי לקח את בנו וגדלו הוא בעצמו כמשפט בני הגויים ונתגדל בגיות, כה"ג אמרינן דאיגלאי מילתא למפרע דהורתו ולידתו בגיות וחשיב כאילו תחלתו גוי גמור, ובאופן זה אינו מותר לבא בקהל עד שיתגייר גירות גמור, דהכי דרשינן ליה לקרא את בתך לא תתן לבנו כי יסיר את בנך מאחרי, דה"פ דבן בתך דקרוי בנך וכישראל מעיקרו מיקרי היינו אם לא יסירנו מאחרי, דאם יסיר את בנך מאחרי דמעיקרא מגדל אותו גוי כמגדל בין הגויים, הרי למפרע אינו קרוי זה בנך.

2.  There is one Achron that holds, or at least, proposes, that the child of a Jewish mother and gentile father is Jewish only after the child is born.  During pregnancy, the fetus is not Jewish.  The child only becomes Jewish at birth.

This is the opinion of Rav Eliahu Poisek (A Ukrainian Rov, see end of post, in his Marbeh Torah on Hilchos Ribbis, end of Siman 159).  It is brought down in the Darkei Teshuva there in Yoreh Dei'ah.  It can be seen here.  This is what he says:

 עי׳ מ״ש בסי׳ ק״ס ס״ק  מ״א דגם בישראלית

 שמת בעלה והניחה מעוברת דיש להסתפק להתיר ללות ולהלות על נכסי העובר ברבית

 ע״ש הטעם כ״ש בנתעברה מעכו״ם ואף אם היא אינה מומרת מ״מ י״ל כמ״ש בהסכמתי

 לס׳ זבר טוב להרה״ג ר׳ זאב פהפערש בהערותי לכורת הברית (דף ק״ל) דאף

 למ״ד דהולד כשר וא״צ גירות דוקא אחר הלידה בישראל . אבל במעי אמו עדיין

 אינו כישראל [דחלקיה קרא זרע אדם וזרע בהמה לחוד חולין ה'] וס״ל  כרב יוסף

 דגם לר׳ יוסי עובר במעי זרה אינו זר עי׳ יבמות ס׳ז ועי׳ רש״י נדה (מ״ד ע״א )  ד״ה

 ולאפוק׳ מדר״י והנפ״מ לענין לחלל שבת עבורו ע״ש [וי״ל בזה קושית הבאר שבע

 בסנהדרין צ״א מב״ר ע״ פ  ויתרוצצו הבנים ע״ש וכן י״ל סתירת הש״ס דביומא צ״ג

 קרו עליה זורו רשעים מרחם ויצא שבתא• ובסנהדרין צ״א משמע דיצה״ר שולט רק

 משיצא לאויר העולם .  די״ל כמ״ש תוס׳ גיטין י״א דשבתאי שם עכו״ם ושם מסתמא

 נתעברה מעכו״ם ואסקי ליה בשמה דאבוהו ובנתעברה מעכו״ם שולט היצה״ר במעי

 אמו ואף לרבינא בסנהדרין ק״י דמשעה שנזרע בא לעוה״ב י״ל דוקא הבא מזרע

 ישראל וכמ״ש ומספר את רבע  ישראל ואכמ׳׳ל] וא״כ ה״נ  לקולא י״ל דהוא כעכו״ם

 עדיין דשרי נכסיו ברבית אף על ידי אפוטרופוס שלו שהוא ישראל וצ״ע:

(This would generate numerous halachic ramifications.  Examples: Ribbis to and from his estate; piku'ach nefesh; whether he can be yoreish at that point; and, most importantly, how many chickens you 'd need for kaparos.)

This is obviously only one Rov's opinion, and would not constitute citation to authority.  In fact, it's not in the sefer that he says he said it in, his כורת הברית, and I think he regretted saying it and took it out.  But I have another surprise for you.  You will see that although Rav Poisek is the only person to say this explicitly, it is clear that there are others that will find themselves painted into the corner with him.

There are Achronim that hold that during pregnancy, the mother is not legally denominated as "mother" of the fetus, but the father is called the "father" as soon as the pregnancy becomes evident.  I'll bet dollars to donuts that these Achronim didn't realize it, but it seems to me that if you accept their svara, then the chiddush of Reb Eliahu Posek is concomitant.  Although the mother's religious identity is dominant over that of the father, that's only once the woman is called the child's mother.  According to these Achronim, during pregnancy there is no legal mother, only a father.  If the father is a goy, then of course the child is a goy.  But once the child is born, and he has a mother and a father, then the mother's religious identity is absolutely determinative.

(I realize that אפקריה רחמנא לזרעיה, Yevamos 98a.  But I don't need for the עובר to be misyacheis to the father to make him a goy.  All I need is that he's not misyacheis to a father who is a Yisrael.  If he has no yichus to a Yisrael father, and he has no mother l'halacha, then by default, he's a non-Jew.)

And who, you ask, are these Achronim?  Are they mischievous Poilishe Pilpul People?  Or obscure Ukrainian Rabbanim?  Nope.  They are Reb Yosef Engel and Dayan Fisher.
Reb Yosef Engel is in his Beis Ha'Otzer, Klal 4, Av, and it can be found here.  Dayan Fisher is in his Even Yisrael on the Rambam in 16 Ishus 7, and can be found here, in the third paragraph.

If you think about it, you'll realize that the Maharshal wouldn't be shocked, either.  If the status of such a child is only fixed if he is raised/acts as a Jew, then there must be a period of pendancy.  His status is to be later determined- at which point his status is retroactive.  Perhaps it's only retroactive to the moment of birth, but not to the moment of conception.

And if you take this to its natural conclusion, what about a Jewish man who fathers a child by a non-Jewish woman?  Would these poskim say that during the pregnancy the fetus is Jewish, and only becomes non-Jewish when it's born?

Anything can happen on Torah Avenue.

Because this is the internet age, and you can find out all different kinds of things about all different kinds of people, here's a paragraph from the Wikipedia article about the Posek family, evidently written by a family member.

Rabbi Hillel Poisic (15.1.1881 Zlatopol,  Ukraine – 1953 Tel Aviv, Israel ) was a communal worker and Torah Scholar.  He was an expert in releasing agunot....

The Poisic (also Poisik, Posek, Possek) family is a rabbinical family originated in the Shapira family and connected to it in marriage relationships. The Poisic members were active in Ukraine.

Rabbi Hillel Poisic's father, Rabbi Elijah Poisic (1859-1932), was one of the most important Rabbis in Ukraine. He served as rabbi in Mohlika and in Zlatopol and composed Responsa and halakhic books about Sukkot, Maimonides and the letter of divorce (get). His expertise was in circumcision law. His mother, Matalia, daughter of Zwi Sonik, was the granddaughter of Rabbi Chaim Chaikel Shapira from Kalininblatt (in Kiev district), father of Rabbi Judah Josef Loeb Shapira, president of the rabbinical court in Rakhimstrivka, and R. Israel Volodarsky, president of court in Petrikovna (in Kherson district). Rabbi Hillel studied Torah with his father and grandfather, Rabbi Moshe Zvi Poisic. He received his ordination  as rabbi by the most important rabbis in south Russia, Rabbi Moshe Nathan Rubinstein from Vinnitsa and the Rabbi Yosef Halperin, president of the court of the Jewish community in Odessa.