Northern Virginia Democrats from the 10th Congressional District yesterday split as expected over who should be the party's presidential candidate, but united in cheers over Democratic Rep. Joseph L. Fisher's announcement that he will seek a fourth term.

Fisher, the region's congressman since 1972, said differences won't amount to much in November when the party is confronted with a Republican challenger.

"Like all families, we feud and fuss some," said Fisher, who represents a district that includes the cities of Fairfax and Falls Church and the counties of Arlington, Loudoun and northern Fairfax. "But we work out our differences and close ranks behind our chosen candidates."

Except for naming the specific national convention delegates, the outcome of the 10th District meeting and four other congressional district gatherings held around the state yesterday was no surprise.

Local party caucuses held around the state last month had already given President Carter almost a 6-to-1 lead over Sen. Edward M. Kennedy of Massachusetts in the contest for Virginia's 64 delegate votes at the national convention in New York City this August.

The 10th District's five national delegates were thus apportioned yesterday so that Carter had three and Kennedy, two. The president also picked up 20 additional delegates from other meetings, while Kennedy's strength yesterday was confined to Northern Virginia.

Northern Virginia's 8th Congressional District and three other districts will hold similar meetings next Saturday.

The three Carter-pledged national delegates chosen to represent the 10th District were Margot Horner, John Schell and John Melnick. The two Kennedy delegates elected were Penelope Rood and Michael Hill. Additional at-large delegates to the national convention will be chosen at the state party convention in May.