Shani Jayanti (शनि जयंती) is the birth day of Shanaishchara, the slow-moving graha, son of Surya and Chhaya. It is kept on the Amavasya of Vaishakha as the Amanta calendar counts the months, the same day that the Purnimanta calendar calls the Amavasya of Jyeshtha.
The Skanda Purana tells, in the Avanti Khanda, that Chhaya bore twins, the river Tapi and Shanaishchara, "who scorches all the worlds". In the Kashi Khanda, Shani is worshipped as Shanaishchareshvara at Varanasi, and whoever sees him there on a Saturday is freed from the affliction of Shani.
The same Purana gives the names of Shani to be recited at dawn: Sauri, Shanaishchara, Manda, Krishna, Ananta, Antaka, Yama, Pinga, Chhayasuta, Babhru, Sthavara and Pippalayana. Whoever recites them, it says, never suffers the affliction of Shani. When an Amavasya falls on a Saturday, it asks for bath, dana and shraddha.
"Sauri, Shanaishchara, Manda, Krishna, Ananta, Antaka, Yama, Pinga, Chhayasuta, Babhru, Sthavara, Pippalayana: whoever recites these names of Shani at dawn never suffers the affliction of Shani."
Skanda Purana, Avanti Khanda 56
Tradition & Practice
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Son of Surya and Chhaya
Chhaya bore twins, the river Tapi and Shanaishchara (Skanda Purana, Avanti Khanda).
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Vaishakha Amavasya
The Amavasya of Vaishakha (Amanta), the same day as Jyeshtha Amavasya in the Purnimanta reckoning.
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Names at dawn
Recite the names of Shani at dawn, and his affliction does not come.
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Saturday Amavasya
When Amavasya falls on a Saturday: bath, dana and shraddha.