Yamuna is connected with Krishna like Ganga with Shiva. Her place of worship is Yamunotri in the Himalayas.
She is considered Yami, daughter of Surya and Samjna.
After Hanuman had burned Lanka he cooled his tail in the snow of the Himalayas. The melting snow became the Yamuna.
The mystical mountain Kalinda is considered to be the source of the Yamuna. As the daughter of Kalinda, she is called Kalindi.
When Indraprastha was built, the Yamuna flowed around the city. Balarama, Krishna’s brother, once wanted to take a bath and asked the Yamuna to come to him. Since she refused, he forced her to do so. Since then the Yamuna has been flowing through Indraprastha, today’s Delhi.
Vyasa was born on an island of the yamuna.
A hymn in honor of Yamuna, the Yamunashtakam
http://stotrarathna.blogspot.com/2009/07/yamunashtakam.html