Although the New Testament is written in Koine Greek, yet there are over ten times in the New Testament that there is a reference to a language which is not Greek. It is also technically not Hebrew. It is known as Aramaic.
Aram is mentioned in Genesis 10:22 as being a descendant of Noah and Shem. There are numerous places where the country of the descendants of Aram are mentioned but regrettably the KJV and several other translations usually use a Roman (latin) word for the people who settled in this land after Nebuchadnezzar defeated the Assyrians at the battle of Carchemish.
(The KJV often uses Latin names instead of the names found in the original text. For example, in Acts 17, Paul is in Athens which is a GREEK city. He is taken up on a hill which the Greeks considered to be sacred to Ares called the Areopagus. The KJV changes this to a reference to the Roman "Mars" even though this was not a Roman culture. "And many such things they do.")
There are some passages, however, which even the KJV does not corrupt. Examples are: Numbers 23:7; 1 Chronicles 7:14 and several others.
The language of the descendants of Aram was known as Aramaic (not Syrian). During the first century, most of the people who lived in Galilee, Samaria, and Judaea who were neither Romans nor foreigners spoke the Aramaic language rather than the Hebrew language of their ancestors.
There are a few places where a derivative of Aramain known as neo-Aramaic has been spoken for centuries but in recent years primarily due to persecutions, the inhabitants of these places have migrated away from their ancestral lands and the language is in danger of dying out.
A recent article on B.A.R.'s website talks about an effort to preserve the Aramaic language. There is a much longer article also available but it is behind a paywall.