Unlike Joseph of Arimathea or Caiaphas, Veronica has no place in the canonical New Testament at all. No Gospel records a woman wiping the face of Jesus on the road to Calvary, and no early Christian writer knows the episode. She is, in the strict sense, a legendary figure, a person created by devotion rather than reported by a source.
Her story is now most familiar from the Stations of the Cross, where the sixth station shows her offering her veil to the suffering Christ and receiving his image in return. This devotion is itself a development of the later Middle Ages; the fourteen stations took their settled form only in the fifteenth to eighteenth centuries, and Veronica's station is part of that growth, not an ancient memory.
The atlas classes her historicity as debated in the precise sense that the tradition itself does not rest on attested testimony: there is a rich cult and a beloved image, but the woman behind them cannot be traced to any early witness. What can be traced is the name, and the name turns out to explain a great deal about how the figure came to be.