Her works, and works in her name, are collected in the Sibylline Oracles.
For the Romans, no set of writings was more important than these various "Sibylline Oracles," which is why the Roman leadership compiled and stored them in the great Temple of Jupiter, where it took an official act of the Roman senate to authorize access to them. They were to be consulted only in the most dire of circumstances.
Alas, the official compilation of oracles was destroyed when the Roman Temple burned down in 83 BC.
Our current set of Sibylline Oracles comes from later attempts to reconstruct the original body of work. As is often the case, the people doing the reconstruction frequently had their own agendas, so we are now left with a mishmash of original oracles and later emendations. These are collected primarily in two major compilations, commonly referred to by scholars as phi (Φ) and psi (Ψ).
Surprisingly, Jewish and Christian leaders, too, respected and even praised the Sibylline Oracles, even though the Sibyl, though claiming to be Noah's daughter or daughter-in-law, is clearly is pagan. The Christian theologian Clemens Alexandrinus even says that St. Paul quoted the Sibylline Oracles when he preached. For the great historian Josephus as well as for early Christian leaders, part of the appeal of the Sibyl was that she provided independent confirmation of what the believers were saying.
2. Gods: Josephus, a Jew, doesn't seem to mind that the Sibyl refers to lots of gods.
3. Four vowels and two consonants: This refers to Jesus's name in Greek: Iesous (Ιησους).
4. Race of most righteous people: The Jews.
6. Prosperous City: Alexandria