Parama Ekadashi is the Ekadashi of the dark half of the adhik (extra) lunar month, so like Padmini Ekadashi it comes only in a year with such a month, about once in three years. Its katha is the story of Sumedha and Pavitra, a poor but generous couple of the city of Kampilya, and of the sage who taught them this fast.
The Ekadashi vrat dates list shows which years carry an adhik month and therefore a Parama Ekadashi; in those years the day's own page there has the parana time for your city. Below is the katha, told in our own words.
The katha
Yudhishthira said, "Krishna, tell me now of the Ekadashi in the dark half of the extra month. What is its name, and what does it give?"
Krishna said, "It is called Parama, the highest. It gives what is good in this world and release beyond it. Listen to what happened to a poor brahmin and his wife."
A poor house that never turned anyone away
In the city of Kampilya there lived a brahmin named Sumedha and his wife Pavitra. They were honest and devout, and they were very poor. Often there was not enough food in the house for both of them. Sumedha begged for alms and sometimes came home with nothing.
Yet in all their poverty they had one rule they never broke: no guest left their door hungry. If a traveller came, Pavitra would give him her own share, and go without herself, smiling as she served. She never let her husband see that she had not eaten, and she never complained.
Sumedha saw her growing thin and could bear it no longer. One day he said, "We cannot go on like this. I will go to some other land and look for work, or for a patron. When I have earned something I will come back. It hurts me to see you go hungry for the sake of our guests."
Pavitra's answer
Pavitra listened, and then she joined her hands. "You are wise," she said, "and I would never stop you from doing what you think right. But listen to me for a moment. What comes to us comes because of what was given before; the wise say that wealth follows giving, not wandering. If we have little now, it may be that we gave little before. Here we have each other, and we have our guests to serve. I would rather go hungry with you here than eat alone while you are far away."
Sumedha was moved, and he stayed.
The sage at the door
Not long after, the sage Kaundinya came to Kampilya and stopped at their house. Sumedha and Pavitra were overjoyed. They washed his feet, gave him a seat, and served him whatever they had, which was little, with great care. Kaundinya saw both the poverty and the grace with which it was carried.
When he had eaten, Sumedha and Pavitra sat before him and asked, "Sage, tell us how this poverty may end. We do not ask for riches, only enough to serve our guests and live without want."
Kaundinya said, "In the dark half of the extra month there is an Ekadashi called Parama. Keep it together, with devotion. Kubera kept it and became the lord of wealth; King Harishchandra kept it and his lost kingdom and family were returned to him. Keep it, and your want will end." He also told them of a stricter way, a fast of five days beginning on that Ekadashi, kept by those who are able.
The fast and after
When the extra month came, Sumedha and Pavitra kept Parama Ekadashi just as Kaundinya had taught, Pavitra with him in every part of it, worshipping Vishnu, fasting, and keeping awake through the night. They kept the longer fast as well.
Soon after, a prince of the land, passing through Kampilya, heard of the brahmin couple who never turned a guest away. He came to their door, and seeing their goodness, gave them a fine house, land and everything they needed. Sumedha and Pavitra lived in comfort from then on, and their door stayed open to every guest as before.
Krishna ended by telling Yudhishthira that whoever keeps Parama Ekadashi in the extra month is freed from want and from the faults of the past, and that even hearing the story brings its share of blessing.
Reading the story calmly
The katha speaks of poverty as the fruit of what one gave or did not give before, an old way of reading hardship that families today hear with care. It is not a judgement on anyone who is poor now; the story's own poor couple are its heroes. The longer fast it mentions is also told as part of the story, not as a test of devotion. A health caveat matters more than tradition here: a five-day fast is not safe for most people, and the single Ekadashi, kept gently, is what nearly everyone keeps.
What the day is kept for
Parama means "the highest". The mahatmya praises this Ekadashi as one that frees from want and gives both worldly comfort and final release, and its examples of Kubera and Harishchandra are part of that praise. These are the text's claims, and households hear them as such.
What people take from the story is Pavitra. Her answer to poverty is not despair or hoarding but generosity, and her answer to her husband's plan is a quiet faith that they will be looked after if they stay true. Many people keep Parama Ekadashi with a gift of food to someone in need, in her memory.
How it is kept
Parama Ekadashi is kept with the usual Ekadashi worship of Vishnu, tulsi, a fruit fast and parana on Dwadashi. Because the story turns on hospitality, many families feed a guest or give grain and food on Dwadashi before they eat. Couples often keep it together, as Sumedha and Pavitra did, and the night is kept awake by some with bhajans and readings from the Purushottam Maas mahatmya. The full order of the day is on the Ekadashi puja vidhi page; anyone older, pregnant, diabetic or unwell should keep only a light fast, and a doctor's advice comes first.
The Ekadashis around it
The other adhik-month Ekadashi, in the bright half of the same month, is Padmini Ekadashi, the story of Queen Padmini and Anasuya. Among the regular Ekadashis, the year begins with Kamada Ekadashi in the bright half of Chaitra. For tithi timings in your city, see the panchang.