Aisa would seem typical of Perugia, of Assisi, Perugia, Bastia and Foligno, with a large stock also in Rome, it could derive from the name of Aisa, a city of Thrace, or even from a nickname based on the term osco aisa (part, portion) , but we must not forget that Aisa is also a name from Greek mythology and that it could therefore be a matronymic form.
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