The Purgatory Heaven and Hell in Koranic verses
The following verses of the Koran mention the Heaven and Hell with reward and punishments existing in the Purgatory:
The day it comes no soul will speak up except with permission, some of them will fell miserable while [other] will be happy. (11/105)
Those who are miserable will be in the fire; they shall (hear) moaning and in it (11/106).
Remaining there so long heaven and Earth will last, except for whatever your Lord may wish. Your Lord is a Doer of whatever he wants! (11/107)
Those who have found happiness will be in the Garden, living there so long as heaven and Earth may endure, except for whatever your Lord may wish, as gift that will never crumble away. (11/108)
The fire! They will be exposed to it morning and evening (40/46)
They will have their provision there both morning and evening (19/62)
Beyond them there lies a barrier till the day when they will be raised up again (23/100)
According to Imam Sadeq (the 6th Shia Imam) the barrier (the purgatory) mentioned in the last verse refers to the grave as a place between the world and the hereafter.
Sources :
"Resurrection" (By Allameh Mohammad Hossein Tehrani)