What is the northernmost city in Texas?

Dallam is the north-western county of the United State of Texas.

Explanation:

Dallam was established in 1876 from the Bexar County and was named after James William Dallam. It has a total area of 1505 square miles. It is located within the 86 District of the Texas House of Representatives. Its county seat is Dalhart.

Out of 10 Texas counties, Dallam resembles in most of north side, which constituted the legendary XIT Ranch. This is still famous for the XIT Museum located at Dalhart, and the annual XIT Reunion and are held on every August' first wide weekend.