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