The sheriff and his deputies have both civil and concurrent criminal jurisdiction. That jurisdiction is in Fairfax County, the City of Fairfax, and the towns of Vienna and Herndon. The Sheriff's Office—in conjunction with local police departments—assists with controlling traffic, issuing traffic summonses, and working with state and local law-enforcement agencies. Additionally, sheriff's deputies aid the county police, the U.S. Marshals Service, and the Federal Bureau of Investigation in a joint fugitive task force that provides apprehension and arrest of felons who face current warrants.
http://www.fairfaxcounty.gov/sheriff/aboutus.htm
The only way they might have jurisdiction outside of the county is picking up a state prisoners in Richmond let's say to bring him back to Fairfax for a court proceeding.