The dragon depicted on the fountain is the symbol of the city. There is a lovely square around it where you can sit and relax.
In the 13th century a dragon was wreaking havoc in Klagenfurt, causing floods that destroyed crossings and threatened travelers along the River Glen. A duke offered a reward for anyone who could capture it, and a brave young man tied a bull to a chain and caught the dragon like a fish.
In 1335 the dragon’s skull was found in a nearby quarry aptly known as Dragon’s Grave. The capital city of Carinthia proudly displayed it in the city’s town hall, and in 1590 Ulrich Vogelsang used it to make what is often cited as the earliest known reconstruction of an extinct animal—it’s attributed to Vogelsang, but it’s more likely an anonymous artist made the sculpture, carved from a single block of chlorite slate. Legend claims 300 men, dressed in all white, carried the six-ton beast to the center of town.
https://www.atlasobscura.com/places/lindwurmbrunnen