Source for discouraging converts

Question

When I was looking through the sources for conversion from Sepharadi posek's I noticed a distinct lack of any mention of discouraging converts. As I kept searching I found Sephardic Rabbis saying what sounded like the exact opposite, that one should ensure that they don't reject converts at all.

Chacham Ovadia Yosef, former chief Rabbi of Israel.

"But we must not push off converts too much. It is not right to cause them pain by rejecting them."

Source: http://www.jpost.com/Jewish-World/Jewish-News/Yosef-Conversion-Courts-are-too-stringent

So where does this idea that Jewish law requires rejecting converts? I haven't found it in the Shulchan Arukh, nor in the Mishneh Torah. Someone told me to look up Yevamot and when I did the English translation seems to also say the exact opposite.

"And they do not overwhelm him with threats, and they are not exacting with him about the details of the mitzvot, i.e., the court should not overly dissuade the convert from converting. Rabbi Elazar said: What is the verse from which this ruling is derived? As it is written: “And when she saw that she was steadfastly minded to go with her, she left off speaking with her” (Ruth 1:18). "

Source: https://www.sefaria.org/Yevamot.47b.7?lang=bi&with=all&lang2=en

So where is the source that Jewish law requires that a Jewish convert be discouraged, or discouraged up to 3 times.

Answer 1

The source for discouraging a convert 3 times is found in the story of Ruth, as explained in the Medrash Rus Rabbah 2:16

שֹׁבְנָה בְנֹתַי לֵכְנָה (רות א, יב), רַבִּי שְׁמוּאֵל בַּר נַחְמָנִי בְּשֵׁם רַבִּי יוּדָן בְּרַבִּי חֲנִינָא, בְּשָׁלשׁ מְקוֹמוֹת כְּתִיב כָּאן (רות א, ח): שֹׁבְנָה, (רות א, יא): שֹׁבְנָה, (רות א, יב): שֹׁבְנָה, כְּנֶגֶד שָׁלשׁ פְּעָמִים שֶׁדּוֹחִין אֶת הַגֵּר, וְאִם הִטְרִיחַ יוֹתֵר מִכָּאן מְקַבְּלִין אוֹתוֹ. אָמַר רַבִּי יִצְחָק (איוב לא, לב): בַּחוּץ לֹא יָלִין גֵּר, לְעוֹלָם יְהֵא אָדָם דּוֹחֶה בִּשְׂמֹאל וּמְקָרֵב בִּימִין.

"Return, my daughters, go" (Ruth 1:12) Rabbi Shmuel bar Nachmani in the name of Rabbi Yudin son of Rabbi Chanina [explains]: In three places it is written here "return" "return" "return" [verses 1:8, 1:11, 1:12] corresponding to the three times we push away a [potential] convert. And if he bothers [trying to convert] longer than that we accept him. Rabbi Yitzchak said "A convert should not stay over outside" (Job 31:32): [this teaches that] A person should always push away with his left and bring closer with his right.

Answer 2

The Rambam (Issurei Biah 13:14) writes:

ואם לא נמצא להם עילה, מודיעין אותן כובד עול התורה, וטורח שיש בעשייתה על עמי הארצות, כדי שיפרושו. אם קיבלו ולא פירשו, וראו אותן שחזרו מאהבה, מקבלין אותן, שנאמר ״ותרא כי מתאמצת היא ללכת אתה ותחדל לדבר אליה״ (רות א׳:י״ח):

This is also quoted by the Shulchan Aruch (YD 268:12), and is based on the Gemara (Yevamot 47b) which says:

ומודיעים אותו מקצת מצות קלות ומקצת מצות חמורות מ"ט דאי פריש נפרוש

Cf. Rashi on the Gemara.

Answer 3

אָמַר מָר: גֵּר שֶׁבָּא לְהִתְגַּיֵּיר, אוֹמְרִים לוֹ: מָה רָאִיתָ שֶׁבָּאתָ לְהִתְגַּיֵּיר? וּמוֹדִיעִים אוֹתוֹ מִקְצָת מִצְוֹת קַלּוֹת וּמִקְצָת מִצְוֹת חֲמוּרוֹת. מַאי טַעְמָא? דְּאִי פָּרֵישׁ — נִפְרוֹשׁ. דְּאָמַר רַבִּי חֶלְבּוֹ: קָשִׁים גֵּרִים לְיִשְׂרָאֵל כְּסַפַּחַת, דִּכְתִיב: ״וְנִלְוָה הַגֵּר עֲלֵיהֶם וְנִסְפְּחוּ עַל בֵּית יַעֲקֹב״. The Gemara analyzes the baraita. The Master said in the baraita: With regard to a potential convert who comes to a court in order to convert, the judges of the court say to him: What did you see that motivated you to come to convert? And they inform him of some of the lenient mitzvot and some of the stringent mitzvot. The Gemara asks: What is the reason to say this to him? It is so that if he is going to withdraw from the conversion process, let him withdraw already at this stage. He should not be convinced to continue, as Rabbi Ḥelbo said: Converts are as harmful to the Jewish people as a leprous scab [sappaḥat] on the skin, as it is written: “And the convert shall join himself with them, and they shall cleave [venispeḥu] to the house of Jacob” (Isaiah 14:1). This alludes to the fact that the cleaving of the convert to the Jewish people is like a scab.

https://www.sefaria.org/Yevamot.47b.5