Paul F. Sheridan, a Fairfax County lawyer with extensive experience in Virginia and federal courts, has received the Arlington Bar Association's strongest endorsement for a vacancy on the Arlington Circuit Court.

About half of the bar association's 318 voting members have cast ballots to rate Sheridan and three other candidates for the seat, to be vacated when Judge Paul D. Brown retires Aug. 31.

Sheridan, 48, received 107 "highly recommended" ratings from the lawyers -- more than twice as many as the next candidate, General District Court Judge Francis E. Thomas Jr.

The other candidates are General District Court Judge Eleanor S. Dobson and Helen F. Fahey, deputy Commonwealth's attorney.

In Virginia, judges are elected by the legislature. The Arlington bar's recommendations have been forwarded to Arlington's five-member legislative delegation, which should make its selection this week, said Del. James F. Almand (D-Arlington).

Although the bar association recommendations are not binding, the delegation usually chooses a candidate who has been approved by the bar.

The Arlington delegation does not plan to interview anyone other than the four rated by the bar, Almand said.

Gov. Charles S. Robb will then make an interim appointment, pending formal ratification during the 1986 General Assembly. The judgeship pays $62,700 a year.