halacha - What is the source for pushing away the convert three times?

What is the source for pushing away the convert three times?

I'm also interested in the exact quote.

Answer

It's in the Midrash [Ruth Rabbah 2:16]:

Rabbi Shmuel bar Nahmani said in the name of Rav Yehudah ben Hanina: Three times is it written [in the Book of Ruth] "turn back", corresponding to the three times that a would-be convert is repulsed;

Ruth 1:8

וַתֹּ֤אמֶר נָֽעֳמִי֙ לִשְׁתֵּ֣י כַלֹּתֶ֔יהָ לֵ֣כְנָה שֹּׁ֔בְנָה אִשָּׁ֖ה לְבֵ֣ית אִמָּ֑הּ יַ֣עַשׂ (כתיב יַ֣עַשׂה) יְהֹוָ֤ה עִמָּכֶם֙ חֶ֔סֶד כַּֽאֲשֶׁ֧ר עֲשִׂיתֶ֛ם עִם־הַמֵּתִ֖ים וְעִמָּדִֽי:

And Naomi said to [Ruth and Orpah], Go, return each of you to her mother's house

Ruth 1:11

וַתֹּ֤אמֶר נָֽעֳמִי֙ שֹׁ֣בְנָה בְנֹתַ֔י לָ֥מָּה תֵלַ֖כְנָה עִמִּ֑י הַֽעוֹד־לִ֤י בָנִים֙ בְּֽמֵעַ֔י וְהָי֥וּ לָכֶ֖ם לַֽאֲנָשִֽׁים:

And Naomi said, Turn back, my daughters; why will you go with me?

Ruth 1:12

שֹׁ֤בְנָה בְנֹתַי֙ לֵ֔כְן ָ כִּ֥י זָקַ֖נְתִּי מִֽהְי֣וֹת לְאִ֑ישׁ כִּ֤י אָמַ֨רְתִּי֙ יֶשׁ־לִ֣י תִקְוָ֔ה גַּ֣ם הָיִ֤יתִי הַלַּ֨יְלָה֙ לְאִ֔ישׁ וְגַ֖ם יָלַ֥דְתִּי בָנִֽים:

Turn back, my daughters, go your way.

but if he persists after that, he is accepted.

Ruth persisted:

Ruth 1:18

וַתֵּ֔רֶא כִּֽי־מִתְאַמֶּ֥צֶת הִ֖יא לָלֶ֣כֶת אִתָּ֑הּ וַתֶּחְדַּ֖ל לְדַבֵּ֥ר אֵלֶֽיהָ:

When [Naomi] saw that [Ruth] was determined to go with her, she stopped [objecting].

-R. Isaac said: …A man should rebuff with his left hand, but bring near with the right.