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.
 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.
The first part of Acts chapter 10 states that Cornelius was a roman Centurion stationed in Caesarea.
*Remember many Israelites were Hellenized during the Greek rule (333-168 B.c) of Palestine and Conformed to the ways of Greek culture
(see 1 Maccabees 1; 2 Maccabees 4).
Rome conquered Greece and became the new world power approximately 168 B.C.
In 65 B.C Roman General Pompey captured Israel and again many Israelites conformed, became roman citizens, and followed Roman culture as well and served in their military
*Paul was an Israelite:
 I am verily a man which am a Jew, born in Tarsus, a city in Cilicia:
a Roman Province which make him a legal citizen of Rome) similar to how America allows citizenship today.
Notes, Explanatory and Practical, on the Acts of the Apostles
 There was a certain man in Caesarea called Cornelius, a centurion of the band called the Italian band,
 A devout man, and one that feared God with all his house, which gave much alms to the people, and prayed to God alway.
 He saw in a vision evidently about the ninth hour of the day an angel of God coming in to him, and saying unto him, Cornelius.
 And when he looked on him, he was afraid, and said, What is it, Lord? And he said unto him, Thy prayers and thine alms are come up for a memorial before God.
Cornelius is an Israelite who was a product of the Diaspora of Israelites scattered throughout the nations; a man who kept the Commandments, prayed to the Most High night and day, and helped his people......
"The word which God sent unto the CHILDREN OF ISRAEL, preaching peace by Jesus Christ: (he is Lord of all)"
"To him give all the prophets witness, that through his name WHOSOEVER (OF ISRAEL) believeth in him shall receive remission of sins."