A Doctor of Philosophy, often abbreviated PhD (or occasionally "DPhil")) was an advanced academic degree awarded in the mid-23rd century.
Elizabeth Dehner was awarded a PhD some time prior to 2265. (TOS: "Where No Man Has Gone Before")
It is unknown if any other doctor seen held this degree. As a psychiatrist, Dehner was likely also an MD.
While it is unknown whether other people with the title "doctor" had this degree, Dr. Leah Brahms was an engineer, a profession that has its terminal degree of "doctor" as one in philosophy. Among others seen was xenobiologist Dr. Kila Marr, who had a degree in a field (biology) that awards PhDs for its terminal degrees as well. A PhD is usually concomitant with original and important research in its respective field – which includes nearly all disciplines aside from medicine, theology, and law, and has been granted as such for a millennium as of the 21st century.