In Volume II of The Church’s Year of Grace, Pius Parsch notes that the stational church for today, Monday of Holy Week, was originally the church commonly known as Chiesa del Domine Quo Vadis – the Church of Domine Quo Vadis.
The station originally was the Church “de fasciola,” which according to an old legend took its origin from an incident during St. Peter’s flight from Rome at the time of Nero’s persecution. This is the story. The apostle had come to the first milestone on the Appian Way when the bandage (fascia) covering his foot-wounds (due to prison chains) became loose. Suddenly the Lord appeared to him. Peter asked, “Domine, quo vadis? (Lord, where are you going?)” Jesus answered, “I go to Rome, to be crucified again.” Ashamed, Peter returned to the city.
This is, of course, the story that provided the inspiration and the title for Henryk Zienkiewicz’s Quo Vadis.
The station for Monday of Holy Week was moved in the tenth century to its current spot – Santa Prassede.
The site for the Canons Regular of St. John Cantius has an excellent article about the ancient tradition of observing the stational churches.