They basically are mainland Italians. Their ancestors were from the town of Pegli in Liguria:
https://en.wikipedia.org/wiki/Pegli - nowadays a suburb of Genoa
In 1541 they left Pegli and settled on the island of Tabarca near Tunisia, to fish for coral:
https://en.wikipedia.org/wiki/Tabarca - they lived here for almost 200 years
Tabarka Island in the 1600s:
https://en.wikipedia.org/wiki/Tabarka#History
https://upload.wikimedia.org/wikiped...th_century.jpg
In the 1730s coral deposits near Tabarca were exhausted and they had to move again.
They found coral near San Pietro Island & asked King of Piedmont-Sardinia to move there.
Finally they settled in San Pietro Island in 1739 and established the town of Carloforte.
Carloforte is named after King Carlo (Charles) Emmanuel III who let them settle there.
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It seems that they have not mixed much with Sardinians, only a little bit.