Kiddushin 4:5-4:8
Kidushin4: 5
אֵין בּוֹדְקִין לֹא מִן הַמִּזְבֵּחַ וּלְמַעְלָה, וְלֹא מִן הַדּוּכָן וּלְמַעְלָה, וְלֹא מִן סַנְהֶדְרִין וּלְמָעְלָה.  וְכָל שֶׁהֻחְזְקוּ אֲבוֹתָיו מִשּׁוֹטְרֵי הָרַבִּים וְגַבָּאֵי צְדָקָה — מַשִּׂיאִין לַכְּהֻנָּה, וְאֵינוֹ צָרִיךְ לִבְדּוֹק אַחֲרֵיהֶן. רַבִּי יוֹסֵי אוֹמֵר: אַף מִי שֶׁהָיָה חָתוּם עֵד בְּעַרְכִי הַיְשָׁנָה שֶׁל צִפּוֹרִי. רַבִּי חֲנִינָא בֶּן אַנְטִיגְנוֹס אוֹמֵר: אַף מִי שֶׁהָיָה מֻכְתָּב בְּאִסְטְרַטְיָא שֶׁל מֶלֶךְ.
From the Altar and upward is not investigated, nor from the Platform and upward, nor from the Sanhedrin and upward.  Anyone whose ancestors were known to have been from the public officials or from the charity collectors may marry off [their daughters] to a Kohen, and it is not necessary to investigate their descent. R’ Yose says: Also one who is signed as a witness in the court of Yeshanah near Sephoris. R’ Chanina ben Antignos says: Also one who is listed in the king’s army.
Kidushin4: 6
בַּת חָלָל זָכָר פְּסוּלָה מִן הַכְּהֻנָּה לְעוֹלָם. יִשְׂרָאֵל שֶׁנָּשָׂא חֲלָלָה — בִּתּוֹ כְּשֵׁרָה לַכְּהֻנָּה. חָלָל שֶׁנָּשָׂא בַת יִשְׂרָאֵל — בִּתּוֹ פְּסוּלָה לַכְּהֻנָּה.  רַבִּי יְהוּדָה אוֹמֵר: בַּת גֵּר זָכָר כְּבַת חָלָל זָכָר.
The daughter of a male chalal is disqualified from marrying a Kohen forever.  [If] a non-Kohen married a chalalah, his daughter is qualified to marry a Kohen. [If] a chalal married the daughter of a non-Kohen, his daughter is disqualified from marrying a Kohen.  R’ Yehudah says: The daughter of a male proselyte is like the daughter of a male chalal.
Kidushin4: 7
רַבִּי אֱלִיעֶזֶר בֶּן יַעֲקֹב אוֹמֵר: יִשְׂרָאֵל שֶׁנָּשָׂא גִיּוֹרֶת — בִּתּוֹ כְּשֵׁרָה לַכְּהֻנָּה; וְגֵר שֶׁנָּשָׂא בַת יִשְׂרָאֵל — בִּתּוֹ כְּשֵׁרָה לַכְּהֻנָּה. אֲבָל גֵּר שֶׁנָּשָׂא גִיּוֹרֶת — בִּתּוֹ פְּסוּלָה לַכְּהֻנָּה. אֶחָד גֵּר וְאֶחָד עֲבָדִים מְשֻׁחְרָרִים, אֲפִלּוּ עַד עֲשָׂרָה דוֹרוֹת, עַד שֶׁתְּהֵא אִמּוֹ מִיִּשְׂרָאֵל. רַבִּי יוֹסֵי אוֹמֵר: אַף גֵּר שֶׁנָּשָׂא גִיּוֹרֶת בִּתּוֹ כְּשֵׁרָה לַכְּהֻנָּה.
R’ Eliezer ben Yaakov says: [If] a non-Kohen married a proselyte, his daughter is qualified to marry a Kohen; [if] a proselyte married the daughter of a regular Jew, his daughter is qualified to marry a Kohen. However, [if] a proselyte married a proselyte, his daughter is disqualified from marrying a Kohen. [This applies to] both a proselyte and freedmen, even until ten generations, unless his mother is of Jewish descent. R’ Yose says: Even [if] a proselyte married a proselyte, his daughter is qualified to marry a Kohen.
Kidushin4: 8
הָאוֹמֵר: ,,בְּנִי זֶה מַמְזֵר” — אֵינוֹ נֶאֱמָן. וַאֲפִלּוּ שְׁנֵיהֶם אוֹמְרִים עַל הָעֻבָּר שֶׁבְּמֵעֶיהָ: ,,מַמְזֵר הוּא” — אֵינָם נֶאֱמָנִים. רַבִּי יְהוּדָה אוֹמֵר: נֶאֱמָנִים.
One who says: “ This son of mine is a mamzer,” is not believed. Even if they both say, concerning the fetus in her womb: “ He is a mamzer,” they are not believed. R’ Yehudah says: They are believed.