Purgatory is often dismissed as being nothing more than a Roman Catholic doctrine that most Protestants do not believe, but does Judaism have a concept of purgatory of a state of purgation in which a soul goes to and if so what is the evidence for such a believe within the Jewish faith?
The concept of purgatory appears to be a situation in which a person is punished for his sins but eventually is redeemed after his punishment is over. As an example we see in Kaddish: Eleven or Twelve
The Talmudic Sages teach that the maximum that a very wicked person is punished in the afterlife in gehinom is 12 months. The public recitation of kaddish shields the departed soul from this punishment. Hence, kaddish is recited during the first year after a parent's passing.
However, the custom is to recite kaddish for 11 months only. Saying kaddish the entire 12 months would give the impression that the deceased was a very wicked person who needs protection the entire 12 months
Thus the Jewish concept of punishment after death appears to be similar to the nonJewish concept of purgatory. The temporary punishment until the sins that a person has committed are atoned for.
We see in Maseches Rosh Hashana at the bottom of 16B that there are three classes of people. The completely righteous are rewarded at once, the completely wicked are punished at once, and those in an intermediate state are punished for their sins until they have completed their atonement and rise up. Art Scroll Rosh Hashana 17a1 footnote 1 states
1 I.e. they cry out from the pain for a short period of time and then they leave Gehinnom (Rashi)
[The purpose of Gehinnom is to rehabilitate a person so that he can merit eternal life in the World To Come. Thus, after the ill effects of sin have been cleansed by the appropriate stay in Gehinnom, the person leaves to enter the World To Come]
There is the Kabbalistic concept of the "beating in the grave" hibbut hakever, חיבוט הקבר. Angels are said to beat the recently dead inside the grave, depending on the wickedness of the deceased. This concept is not strongly associated with a limited time-period or punishment, but the whole area of afterlife in Judaism is not standardized and often left unclear.
See also Hebrew Wikipedia,