In what year did Washington City, the original twenty mile square diamond shaped, “District of Columbia” lose all the land in Virginia, including Arlington and portions of Alexandria? Eric showed a neat example of a Washington City bank note from a Virginia town.
The event in 1846 that returned Alexandria County (which was renamed Arlington County in 1920) and the City of Alexandria was called "retrocession."
There are D.C. obsoletes that specified that they would be redeemed in Virginia bank notes, but not the other way 'round. Virginia had a reputation as having a strong and secure banking system, whereas D.C. did not. So, some D.C. banks would specify redemption in Virginia notes to encourage their acceptance.
Now, there were several notes issued in Alexandria while it was part of D.C. (like that 25¢ scrip from the War of 1812 period), but that may be a few dozen issuers at most. Some of the banks opened in Alexandria while a part of D.C. rechartered themselves after retrocession under a different name (the Potomac Bank comes to mind: it became a branch of the Exchange Bank of Virginia). This is why I love our local numismatic history, it's not straightforward!