Acts 10:1
[1] There was a certain man in Caesarea called Cornelius, a centurion of the band called the Italian band
 
 Centurion – occupation NOT nationality
A centurion was a professional officer of the Roman army after the Marian reforms of 107 BC.

 Caesarea Maritima – was built approximately 20–10 BCE near the ruins of a small naval station known as Stratonos pyrgos (Straton's Tower), founded by Straton I of Sidon. It was likely an agricultural storehouse station in its earliest configuration. In 90 BCE, Alexander Jannaeus captured Straton's Tower as part of his policy of developing the ship building industry and enlarging The Hasmonean kingdom. Straton's Tower remained a Jewish settlement for two more generations, until the area became dominated by the Romans in 63 BCE, when they declared it an autonomous city. The pagan city underwent vast changes under Herod the Great, who renamed it Caesarea in honor of the Roman emperor, Caesar Augustus. This small naval station was guarded by Centurions.  

Many people get hung up on the statement that Cornelius was from the “Italian band”… but we are about to find out that the Israelites resided in Rome and other European countries.

Acts 18:2
[2] And found a certain Jew named Aquila, born in Pontus, lately come from >>Italy<< with his wife Priscilla; (because that Claudius had commanded all Jews to depart from Rome:) and came unto them.

This is going to set the record straight on all the confusion that Cornelius was NOT an Israelite. Among the Roman empire there were many Israelites that had Roman citizenship, and were called Italian and Roman.