The province in view is the Trans-Euphrates, which means, beyond the river.
When Cyrus conquered Babylon in 539 BC, he appointed Gubaru as governor of Babylon and the land beyond the river. This became the official title of the fifth satrapy (Ezra 5:3; Ezra 6:6; Nehemiah 2:7).1
16 We make known to the king that if this city is rebuilt and its walls finished, you will then have no possession in the province Beyond the River.”