Padmini Ekadashi is the Ekadashi of the bright half of the adhik (extra) lunar month, and so it comes only in a year that has such a month, roughly once in three years. Its katha tells of King Kritavirya and Queen Padmini, who had no child, and of the advice Padmini received from Anasuya, the wife of the sage Atri.
Which years have an adhik month, and so a Padmini Ekadashi, is shown on the Ekadashi vrat dates list; when it does come, its own page there gives the parana window for your city. What follows is the story in our own words.
The katha
Yudhishthira said, "Krishna, there is a month that is added to the year now and then, the extra month. Tell me of the Ekadashi in its bright half. What is it called, and how is it kept?"
Krishna said, "It is called Padmini, and the extra month is dear to me above all others, for it is mine, Purushottam. Listen to a story that the sage Pulastya once told."
A king without an heir
In the age of Treta there ruled in the city of Mahishmati a king named Kritavirya, of the Haihaya line. He had many queens, and he loved them and they loved him, but not one of them had borne him a child. The king had done everything a king could: given gifts, honoured priests, worshipped the gods. Nothing had come of it.
At last Kritavirya decided that if rites could not help him, penance might. He handed the kingdom to his ministers, put on the bark garments of an ascetic, and set out for the forests of Gandhamadana to practise austerity. One of his queens, Padmini, a princess of the Ikshvaku line, would not let him go alone. She left her ornaments behind and followed him.
On that mountain the two of them lived through many years of hard penance. They ate little, slept little, and turned their minds to God. The king grew thin, so thin that his bones could be seen. And still no child was promised to them.
Padmini goes to Anasuya
Padmini watched her husband wasting away and grew afraid for him. She thought: our way is not working, and he will not stop. I must find another.
Not far away lived the sage Atri and his wife Anasuya, whose devotion was so great that the stories say even the gods came to her as children. Padmini went to her, bowed, and told her everything. "My husband has spent years in penance for a son, and it has brought him nothing but suffering. Tell me some vow that would please Vishnu, so that he grants us a child."
Anasuya listened kindly. "There is a month," she said, "that comes once in some thirty-two months, the extra month, which belongs to Vishnu as Purushottam. In its bright half is an Ekadashi. Keep that fast with your whole heart, and Vishnu himself will come to you."
She told Padmini how. On Dashami she should eat once, simply, and sleep on the ground. On Ekadashi she should bathe at dawn, worship Vishnu with flowers, incense, lamp and offerings, and keep the whole day in fasting and prayer. Through the night she should stay awake, singing and listening to the stories of the Lord, and offer worship in each watch of the night. On Dwadashi, after worship and charity, she should break the fast.
The boon
Padmini went back and kept the fast exactly as Anasuya had told her, with the king's blessing. When the night's vigil was done, Vishnu appeared before her, seated on Garuda, and said, "I am pleased with you. Ask what you wish."
Padmini bowed and said, "Grant my husband a son, Lord." Vishnu smiled and said she should ask him herself, and he turned to Kritavirya. The king, overjoyed, asked for a son who would be unconquered by gods, men or demons, and who would be honoured in all the worlds. Vishnu granted it and vanished.
The king and queen returned to Mahishmati. In time Padmini gave birth to a son, Kartavirya Arjuna, who grew into one of the mightiest kings of the old stories. He is remembered with a thousand arms, and it is said that even Ravana could not stand against him.
Krishna ended by telling Yudhishthira that whoever keeps Padmini Ekadashi in the extra month, and whoever hears its story, shares in the grace that came to Padmini.
Reading the story calmly
The story praises long penance and then quietly shows its limit: the king's austerities wore him down and brought no answer, while his wife's single day of devotion did. Families today hear in that a caution against punishing the body in the name of faith. The king's longing for an heir belongs to its time; the day is kept now for children of any kind, and for the health of the family.
What the day is kept for
The mahatmya says that the adhik month is Vishnu's own, and that the Ekadashi of its bright half gives the merit of all the year's fasts together, with children, fame and peace in this life. These are the words of the text, in praise of a rare day.
Because it comes only in an adhik month, people who keep Ekadashi regularly look forward to it. For many it is the high point of Purushottam Maas, a month already given to extra reading, charity and worship of Vishnu.
How it is kept
Padmini Ekadashi is kept like other Ekadashis, with worship of Vishnu, tulsi, a fruit fast and parana on Dwadashi, and with Anasuya's advice in mind: a simple meal on Dashami, worship through the day, and the night kept awake with bhajans by those who are able. Many add a reading of the Purushottam Maas mahatmya or the Bhagavad Gita, and some couples hoping for a child keep the day together, as Padmini kept it with her husband's blessing. The full order of the day is on the Ekadashi puja vidhi page; anyone pregnant, unwell or older should keep a light fast, with a doctor's advice first.
The Ekadashis around it
The other adhik-month Ekadashi, in the dark half of the same month, is Parama Ekadashi, the story of the poor brahmin Sumedha. Among the regular Ekadashis, the last of the lunar year is Papmochani Ekadashi. The tithi for your city is in the panchang.