The meaning of the word “Jew” has changed over time, and we need to be careful in applying the meaning from one period to a passage written at a different period.
Up until the exile, “Jew” meant somebody from the tribe of Judah. There are hardly any occurrences of this in Scripture; one exception is 2 Kings 16:6.
During and after the exile, it came to mean anybody from the area of Judea, regardless of their tribe. This is evident in Ezra 4:12, for example, where the term includes people of the tribe of Benjamin and Levi (see the list in Ezra 1). Also in Esther 2:5-6 where Mordecai of the tribe of Benjamin is called a “Jew”. By the time of the captivity, the word “Jew” also included converts to the Jewish religion (e.g., Esther 8:17).
By New Testament times, it meant anybody of Israelite heritage as well as anybody of the Jewish religion (e.g., Gal 2:13-15)
The word seems to have an additional meaning in John’s gospel where it often refers to the Jewish leaders. For example, John 5:10-18; 7:13; 11:8; etc.
For further information, see the Wikipedia article on the etymology of “Jew”.