Ovid and Petronius are good sources for the striga, the Roman witch. These were creatures of legend thought to be cursed at birth or afterwards. They were greatly feared and were regarded as anti-social (Petronius recounts a legend describing Roman witches abduct an infant along the lines of later European elfin changelings). The early church discouraged belief in these entities. As one of our redditors is fond saying "there were no witches": he will happen upon this so we will find out if we (in question or answer) have crossed the academic lines he has drawn.

Of course, all cultures have magical practices of some sort (whether it is as simple as wishing on a falling star or birthday candles or touching/knocking on wood). And some people in various societies became or have become known for exceptional abilities in this regard. In most cases, these sorts of people were not linked with the legendary concept of a demonically-allied person known as striga or witch. In other words, these everyday people (regardless of what their peers called them), with reputedly-modest abilities when it came to magic, lived ordinary, everyday lives without prejudice.

During the famous witch craze, things were turned on their heads resulting in widespread accusations, trials, and punishments, but this was a late medieval phenomenon. And this episode caused a blurring between the modest everyday practitioner of magic and the demonically-associated witch of legend. We must point out that there is no verified case of the latter existing even if torture precipitated confessions. Once things settled down, the village practitioner resumed his or her lives, and some of these people were called and may have called themselves witches, but they would never have conceded any demonic relationship. I am doing work with the so-called "pellar families" of Cornwall, particularly studied by a young scholar named Jason Semmens who has published on the subject. These families provided cures and other things based on magical practices, but they were not feared and were not regarded as demonically associated.

Magic is omnipresent in ancient Rome, but the magical powers are believed to come not from the people themselves but from deities or from the dead. Cursing tablets, asking the dead for help have been found from time to time in graveyards at least through the eastern roman world. In fact they are a great source for social relations in the ancient world because they have survived when every other similar sources decayed.

Now were there "persecutions". From what I know I don't think so, except that expulsions of astrologers from Rome were made on some occasions, mostly due to wrong/bad predictions. This resulted in some executions, at least one under Claudius. Those expulsions had surely no influence on the global population in general.

The witch/sorcerer is also a common theme in roman litterature in the imperial period, it's even the center of the Golden Ass of Apuleius. This theme even influenced more recent masterpieces: the story of Mickey as the wizard apprentice, depicted is Fantasia is an adaptation of the same story by Goethe. The german writer didn't created it but adapted to a more european situation an identical story written by Lucian of Samosatus in the second century. The original being about an egyptian magician teaching a spell to make the stone alive to work. As I though of it, there is perhaps a link with the Ushabtis, the egyptian statues put in the tombs to work for the deceased in the afterlife.