This is the first time early voting has been tried for a primary in an odd-numbered year, in which federal and state offices are not on the ballot.

In the Republican primary for sheriff, Healy-Case and Garcia vie to outdo each other in proclaiming loyalty to Donald J. Trump.

The move followed what Mayor Byron Brown described as a “passionate plea” from University Council Member Rasheed N.C. Wyatt in a Facebook post Thursday.