The twin brothers Saint Cosmas and Damian (martyred ca. 287) were physicians and early Catholic martyrs born in Cilicia, part of today's Turkey. They practiced medicine for free as an act of Christian charity. Their medical ministries led to many conversions to the Catholic Faith.
They were made famous by a miraculous operation in which they transplanted an Ethiopian's leg onto a white man's body. This miracle is often celebrated in Catholic art depicting the twin saints.
During the persecution under Diocletian, Cosmas and Damian were arrested by order of the Prefect of Cilicia who ordered them under torture to recant. However, they stayed true to their faith, enduring being hung on a cross, stoned and shot by arrows and finally suffered execution by beheading.
Saint Cosmas and Saint Damian, pray for us.
While we're on the topic of medical doctors, here are the other patron saints of physicians: St. Luke, St. Pantaleon, St. Raphael the Archangel.