The fountain in the Piazza di Santa Maria in Trastevere is considered to be the oldest monumental fountain in the city. Its present version is the work of Bramante, though famous artists like Carlo Fontana and Bernini made later additions.
Piazza Santa Maria in Trastevere Fountain Rome

Though it appears on a 1471 city map made by Pietro de Massaio, it is thought to have replaced a much older (8th century) one.
The fountain was restored many times in the course of the centuries. The first time this happened was towards the end of the 15th century, as the epigram on a plaque on one of its corners testifies.
At the time Trastevere was one of Rome’s poorest districts and the water supply was rather scarce. This situation was remedied in 1659 by Alessandro VII Chigi who commissioned Bernini to increase the supply of water (and add inscriptions and the Chigi coat of arms).
Bernini did not modify the monument’s upper part, but had the octagonal basin raised on steps and added the four double shells (at the time facing outward).
In 1692 Pope Innocent XII ordered that the capacity of the basin be increased and had the shells moved inwards.
Almost two centuries later (1873) the Municipality of Rome had the travertine marble replaced by bardiglio, leaving the structure of the fountain intact however.