You may know, because you already have some documents, where the ancestor you wish to claim as qualifying you for Italian citizenship was born. However, sometimes family stories or genealogy quests are confused by not reading the fine print, so to speak.
For instance, a ship record may ask where the person was LAST LIVING or WHERE THEY LEFT, which could be a seaport. That does not mean that they were BORN at this same location. Some immigrants got to the seaport and lived and worked there a while to earn their tickets for the ship. And as many Italian men were seasonal workers in America before deciding to remain and claim citizenship, you might find the same person going back and forth and information differing from one ship record to the next. Of course these records can be valuable. They may be consistent. One might mention a large city. Another a village near that large city. So get your maps out and look.
There may be a mention of relatives such as a cousin on the ship or a wife left behind.
Once the decision was made to become a citizen, a DECLARATION OF INTENT will have been filed. For naturalization, to become an American, the clock starts ticking with these "first papers."
Perhaps you have their NATURALIZATION / American Citizenship papers which give more details. With the realization that these are official and governmental papers, immigrants are more likely to record accurately where they were born. The naturalization papers might say that they renounce Austria - which could mean they were born in what is now Poland, Slovakia, Hungary, Yugoslavia, or Italy. But they should still give the name of a village, town, or city.
Do some research on that region. What is it's history? When did it become part of Italy? Were there any changes in borders and when? At the time that your qualifying ancestor was born, was that place Italy?
Even if it was not, you may still qualify for Italian Citizenship. You'll just have to keep doing your research.
C 2020 Ancestry Worship - Genealogy BlogSpot
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As a side, years ago while doing some Italian genealogy for a client, I came across an odd situation. Knowing that Italian men sometimes came and went as seasonal workers in the United States, I felt pretty sure that the ancestor had come over three times before settling in Brooklyn. The man, with same name, first and last, the same height, left the same town, left the same port, on the same ship line. On trip one and two, about a year apart, I felt sure this was the same man. On trip three, another year later, it seemed to be the same man but for one detail. This man was noted to have a massive scar on his forehead. The client said there was no way that man was from their family. But before it was all over, they admitted their family had been in organized crime in Italy and in America.