During the Middle Ages, Jews became prominent as doctors, but it took a few centuries for this to happen. There was no real Jewish medical tradition, apart from common sense patient care.
The first step toward Jewish medicine was that Jews in the Arabic world began translating books into Hebrew, so that Jews in Europe could read them. In 800, the Caliph of Baghdad had ordered his new House of Books to buy and translate every book they could find. This project became the main way that a lot of Greek literature was preserved when its original cities were sacked or burned. We have Euclid’s Geometry only as translated back out of Arabic into Greek and Latin.
During the 11th and 12th centuries, enterprising Jewish scholars who spoke Arabic as a first language were involved with Christian efforts to translate Arabic medical books into Latin. Naturally, they also produced Hebrew renditions. Toledo was a center of this translation activity, because Spain had such a large Jewish community that spoke Arabic as a mother tongue, learned Hebrew at home and synagogue, and studied Latin in school. Maimonides’ medical books in Hebrew were primary sources for Jewish study.
The most prestigious doctors held the “laurea” degree from universities, but these schools did not admit Jews during most of the medieval period. All doctors, university-trained or privately schooled, had to pass licensing exams. Each city had a medical examining board composed of two or three Christians. Aspiring physicians had to give lectures and explanations of material in medical textbooks and answer other questions. They could be licensed with limitations if the board was uncertain of their skill; for example, a Jewish doctor with a limited license might be required to practice in partnership with a Christian, or a young doctor with an older, more experienced one, or the license might specify the areas of medicine in which the board felt the holder was competent.
A licensing process like this was personally biased against Jews, but it also was reasonably objective. If a man studied privately with an established doctor, the board did not discriminate against this education if he could pass their exam. That’s where it all came together for Jewish doctors, because their distant relations in the Arabic world could provide them with textbooks, and their families could arrange mentoring, sometimes through marriage to a doctor’s daughter. Medicine became a sort of family dynastic practice.
Outstanding Jewish doctors were richly rewarded by Christian city or national rulers. They were paid a lot, of course. Additionally, they could be given special exemptions from taxes or rules imposed on other Jews. Some got permission not to wear weird pointy yellow hats or other distinctive clothing. In some cases, the secular rulers sent word to synagogues stating that the favored doctor should be given precedence in the service. There’s no question that “My son, the doctor” became an exceptionally important bragging point.