Fairfax County Board Chairman John F. Herrity went to the top yesterday in his effort to kill a Justice Department discrimination lawsuit against the county, telling President Reagan that federal workers are harrassing county workers in a "fishing expedition" to sustain the suit.

"I must strongly object to the Justice Department's tactics in this matter," Herrity said in letters to the president and Attorney General William French Smith. "I would further describe such a 'fishing expedition' as an abuse of federal authority and of questionable ethics."

What angered Herrity were reports that at least seven Fairfax County workers have been telephoned at home by Justice paralegals as late as 11 p.m. in the last three days. The callers asked if the employes knew of any bias or discrimination by county officials. In at least one instance the caller refused to identify himself for several minutes, according to a Fairfax official.

Herrity, referring to Justice investigators as "shysters" in an interview yesterday, said the department should investigate its handling of the case and suggested the judge hearing it should issue an order restricting the department. The Fairfax Republican, who has predicted that the Reagan administration would be willing to drop the lawsuit, also likened the department's behavior to that of a lawyer "dropping your card at the scene of an accident."

Herrity's letters represented his latest effort to quash a lawsuit the Justice Department filed against the county in December 1978 accusing it of discriminating against women and minorities in its employment practices, allegations that Harrity has strongly contested.

A District Court judge largely rejected the charges in 1979, but an appeals court overturned that ruling and sent the case back to Alexandria federal court, indicating that the judge hadn't fully considered the Justice Department's complaint. It is scheduled for retrial on March 17.

In his letters, Herrity noted the original trial had cost Fairfax taxpayers more than $200,000 and said the retrial would increase county legal expenses by $100,000 or more. "In your recent election campaign you promised repeatedly to 'get the federal government off the backs of local and state governments,'" Herrity told the president. "This most recent instance of harrassment by the Justice Department is a case in point."

Ronnie Edwards, a Justice paralegal with the civil rights division who Fairfax officials said made some of the calls, declined comment yesterday. But Justice spokesman John Wilson said, "If employes are being contacted late in the evening, it will cease . . . and that comes from the supervisor in charge of the Fairfax case."

The supervisor, David Rose, said, "I know the great majority of the calls were made in early evening. Our conduct in court is prescribed by federal rules and procedures. This is our general practice," Rose said future calls would be made before 8:30 or 9 p.m.

"This is not particularly unusual. We've got a client and a case. We're trying to find out what the facts are," Rose said.

Herrity, however, said he was incensed that the phone calls were being made at all.

"I have a lot of friends who are lawyers and if they didn't have enough evidence for a case they didn't go to trial," Herrity said in yesterday's interview.

The county, which established an affirmative action program in 1977, sought yesterday to underscore its contention that it does discriminate with figures from a new report on recent hiring.

In the last six months of 1980, 14 percent of those hired by the county were miniorities (67 of 468) and 49 percent were women, the report said. The report also said minorities now make up 16 percent of the county's paraprofessionals, as opposed to 13 percent in December 1979.

In his letter, Herrity cited as a further "instance of questionable ethics" letters he said were sent by Justice to black churches in Fairfax several months ago seeking information about alleged bias. The department got "absolutely not one bite" from them, Herrity said.