A hundred years after this destruction, in 44 BC, Julius Caesar rebuilt Corinth as a Roman city. After all, it was still a very good port! The Romans built many new buildings in Corinth in the Roman style. The early Christian preacher St. Paul visited Corinth about 50 AD, and gave a series of speeches there to convert the Corinthians to Christianity. Corinth lasted as a Roman city throughout the Roman Empire, although it was attacked by Herulians (Germanic invaders) in 267 AD, and by Alaric the Visigoth in 395 or 396 (and Alaric sold many people who lived in Corinth into slavery).
Corinth was still a city in the Byzantine Empire, although a terrible earthquake in 521 AD did a lot of damage. By the 1400s Corinth had been taken over by the Ottoman Empire, where it was no longer an important city.
Wealthy Corinth: A History of the City to 338 BC, by J. B. Salmon (1984). Readable.
St. Paul’s Corinth: Texts and Archaeology, by Jerome Murphy-O’Connor (second edition 1990). See what ancient Greeks and Romans had to say about Corinth in the time of St. Paul, in their own words (translated into English).