Montgomery County Sheriff James A. Young survived a count of absentee ballots yesterday to win nomination to a new term in office by 308 votes out of almost 60,000 cast in Tuesday's Democratic primary.

Challenger Tony Fisher conceded defeat last night after hearing the final tally of 30,107 votes for Young to 29,799 for himself. Fisher declared he has no intention of running for the office again, adding: "We are just satisfied to know that because of our campaign people now know more about what the sheriff does. We believe our campaign has helped improve the overall management of the Sheriff's Department."

In November, Young, 58, appointed to the post six years ago, will face opposition from Republican Jerry O. Anderson, who easily defeated William J. Neptune in the GOP primary.

When the Democratic ballots cast at the polling places were counted Tuesday night, Young held a 784-vote lead and claimed victory. Fisher's concession came only after 2,072 absentee ballots were counted.

Fisher, 32, a 12-year veteran of the county police force, waged an energetic and well-organized campaign against Young, whose personal campaigning was slight by comparison.

One of the many allegations Fisher made was that Young is a poor administrator who mismanaged about $200,000 in fees paid to his office and cost the county $30,000 in interest that the money could have earned.

Young denied the problem Fisher cited was caused by mismanagement on his part and said the problem was corrected several months ago and that county funds his office collects are now handled properly.