From Kurd Net:
Asenath Barzani from Iraqi Kurdistan region [South Kurdistan] was the first known woman rabbi in Jewish history.
There are not many female rabbis in the Jewish history. The first known female rabbi in the history is Asenath Barzanî, a Kurdish woman from South Kurdistan.
Regina Jones who was officially declared rabbi in the German capital Berlin in 1935 used to known as the first female rabbi in the Jewish history. However, this information corrected recently by historian who unveiled documents indicating that a woman called Asenath of Barzani region in South Kurdistan was declared as rabbi in the 17th century.