Ashurites
The Ashurites are named once in the UPDV — in the list of territories over which Abner installs Ishbaal as king.
Among Ishbaal's Domains
After Saul's death, "Abner the son of Ner, captain of Saul's host, had taken Ishbaal the son of Saul, and brought him over to Mahanaim; and he made him king over Gilead, and over the Ashurites, and over Jezreel, and over Ephraim, and over Benjamin, and over all Israel" (2 Sa 2:8-9). Ishbaal's reign — "Saul's son, was forty years old when he began to reign over Israel, and he reigned two years" (2 Sa 2:10) — is set against the parting allegiance of Judah, which "followed David" (2 Sa 2:10).
The Ashurites appear in this list between Gilead and Jezreel; the text supplies no further description of them or of where exactly they are.