The Fairfax County Board of Supervisors yesterday called for a study by Virginia court officials of proposed changes in the county's magistrate system that could force the father of one board member out of a job.

In a unanimous vote, the board asked the state to expedite a study of the changes under which the state would take over administration of Fairfax's 37 full- and part-time magistrates at a saving to the county of $615,000 annually.

Board members left open the possiblity they would decide this year to join the state system despite statements by county staff members who cautioned the study might not be completed in time for the General Assembly to appropriate the necessary state funds during its current session.

Among those favoring a delay until next year was Joseph Alexander (D-Lee), who said he felt it would be advisable in order to give both the county and the state ample time to study the proposal.

A beneficiary of the present system is Alexander's father, chief magistrate Milton Alexander, who is 71, one year past the mandatory retirement age for full-time magistrates under the state system.

The elder Alexander, who earns $21,370 a year, is now affected by neither state nor county rules that set mandatory retirement at 70. Virginia court officials have said that even under a state takeover in Fairfax, Alexander might retain his position if a grandfather provision were approved by the legislature.

Audrey Moore (D-Annandale) argued yesterday the county should press the state to complete its study in time for county action this year.

"I do realize this is a delicate issue, and I certainly understand the personal feelings involved in this," Moore said in an apparent reference to the Alexanders. But , she said, the possibility of a big saving to the county require the supervisors to "at least . . . give ourselves the option" of joining the state system this year.

Supervisor Alexander, who voted for the study, has said his objections to a state takeover stem from his belief that there would be a reduction in the serivces now provided to do with his father. The chief magistrate is appointed by the county's chief circuit court judge, Barnard F. Jennings, who has praised Milton Alexander's work.

In other action yesterday, the supervisors appointed David T. Stitt as county attorney at an annual salary of $44,303. Stitt, 36, has been acting county attorney since the resignation last November of Frederick L. Ruck.

A member of the county attorney's staff since 1975, Stitt previously served as an assistant U.S. attorney in Washington and as an assistant corporation counsel for the District of Columbia. He received his law degree from the University of Texas School of law in 1969.