St. Perpetua is well-known as a martyr from the 2nd century and her account of martyrdom is preserved in what's called the The Passion of the Holy Martyrs Perpetua and Felicity.
Included in this account is a vision she had of her deceased brother, and many commentators believe she saw purgatory.
Without delay, on that very night, this was shown to me in a vision. I saw Dinocrates going out from a gloomy place, where also there were several others, and he was parched and very thirsty, with a filthy countenance and pallid color, and the wound on his face which he had when he died...And moreover, in the same place where Dinocrates was, there was a pool full of water, having its brink higher than was the stature of the boy; and Dinocrates raised himself up as if to drink. And I was grieved that, although that pool held water, still, on account of the height to its brink, he could not drink. And I was upset, and knew that my brother was in suffering. But I trusted that my prayer would bring help to his suffering.
Purgatory is believed to be a place that prepares a soul for Heaven and various saints have had similar visions of a type of suffering present in this place.
Praying for souls in purgatory
St. Perpetua then had a follow-up vision where she saw the fruit of her prayers.
Then, on the day on which we remained in fetters, this was shown to me. I saw that that place which I had formerly observed to be in gloom was now bright; and Dinocrates, with a clean body well clad, was finding refreshment. And where there had been a wound, I saw a scar; and that pool which I had before seen, I saw now with its margin lowered even to the boy's navel. And one drew water from the pool incessantly, and upon its brink was a goblet filled with water; and Dinocrates drew near and began to drink from it, and the goblet did not fail. And when he was satisfied, he went away from the water to play joyously, after the manner of children, and I awoke. Then I understood that he was translated from the place of punishment.
This vision from the early Church confirms what Catholics believe when it comes to purgatory and how our prayers for deceased family members can have a real effect.