There *are* left-handed violins and left-handed violinists but they are not common; mostly because opposite-handedness can cause problems when playing in an orchestra. And an overwhelming majority of professional violinists play in an orchestra. Most violin teachers go to great lengths to force left-handed people to only learn how to play right-handed.
Here is one site that lists several famous left-handed violinists.
As to any music written to be played specifically for the left hand there are examples of pizzicato music written for the strings to be plucked with the left hand. Niccolo Paganini wrote two particularly famous ones - 'Caprices' and a variation on 'God Save the King'.
Often cited as the hardest works for solo violin, Niccolò Paganini’s Caprices make up 24 fiendishly demanding pieces for the string instrument, packed with double stops, left-hand pizzicato and endless spiccato bowing. It’s no wonder people thought Paganini was in league with the devil…
In 1829, Paganini decided to compose a highly virtuosic set of variations on the theme of England’s national anthem, ‘God Save the King’, featuring his signature techniques of left-hand pizzicato and spiccato aplenty. https://www.classicfm.com/discover-music/instruments/violin/hardest-pieces-for-violin/
However, other than 'pizzicato'or similar methods, playing a violin requires the use of both hands; one to hold the instrument and vary the pitch of its strings, the other to 'draw' the bow. While they may exist, I've been unable to find any examples of music written specifically to be played by a one-handed violinist.