I have seen Fairfax County Police stop cars on I-66. I thought the interstates are under the jurisdiction of the Virginia State Police.
By tradition, the Virginia State Police patrol the interstates and leave the County roads to the Fairfax County Police. In fact, both have Jurisdiction. Virginia State Police have jurisdiction on every road in the state, and the County have jurisdiction on every road in the County. Normally, the State Police will handle accidents on the Interstates, but sometimes it is just a matter of who gets there.
In many rural Counties, there is no county-wide police force, so enforcement is left to the State Police and Sheriff.
In Fairfax County, the Sheriff and deputies can also make stops on any highway in the County.
We have many other police agencies as well. I have had clients stopped by Campus Police, Metro Airport Police, Metro Transit Police and federal agencies as well. Also, the ABC and DMV have officers who also have cars that can make a traffic stop.
Beware of some of these "Wannabee" cops. Some folks will see a different type of police car and go right back to speeding, only to be surprised that the Airport police can stop people even if they are not at the airport.