Only 0.5-1% of Italians are descended from foreigners who migrated during the Roman period

This is exceptionally in agreement with specific haplogroups.

According to historian David Noy, the number of foreigners in the city of Rome - which would have been much higher than elsewhere in Italy - was only about 5% at its maximum. And these foreigners (especially slaves) had higher death rates and lower birth rates than the natives, and were sometimes even subjected to mass expulsions.

Furthermore, half of the main areas they came from were other parts of Europe adjacent to Italy: Gaul (France), Hispania (Spain and Portugal), Central Europe (Southern Germany), Eastern Europe (Balkans), and Greece. And even those outside Europe were predominantly of Greek descent, while the Jewish ones never fully assimilated into Roman society, remaining an identifiable minority. If the percentage of foreigners at its highest in Rome was 5%, it was certainly extremely lower elsewhere, and the high mortality rates, coupled with the almost total superfluous nature of "recent" explanations for almost all haplogroups, is very likely in general, an Italian from a particular region has about 0.5-1%, with the exception of Lazio, where it is probably around 4-5%. We are talking about the Roman period, but even considering the Middle Ages the percentage at the same time as the Roman period will be very marginal. About 2.5-3% of a typical Italian's ancestors will have been outside Italy in 500 BCE

There is often a study used to prove much higher percentages, but this study only considered samples of the immediate Rome in essence and did not actually identify anything Levantine that cannot be explained by a massive migration of Calabrians and Sicilians and Southerners in general in Rome.