My husbands grandmother was Rose Iodice from Portico Di Caserta. We always thought the last name was Jodice until through our research we found out that there really isn't a letter J in the Italian Alphabet. Now we can read clearly it is Iodice.
In the town of Portico di Caserta there are many many families by this name in the records. I have been studying the microfilm of the Civil records of that city.
On your father's birth certificate where it lists his father's name it might tell how old his father was at that time. That might give you a year or two to search for his birth certifcate to find his parents.
Good luck
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thanks
Valerie