Vaccine distribution, testing options expand in Leon County More people will soon have access to vaccines as Leon County works out a new scheduling system on their website. and last updated 2021-01-07 18:37:24-05 LEON COUNTY, Fla. (WTXL) â More people will soon have access to vaccines as Leon County works out a new scheduling system on their website. Right now, DOH is not accepting any new appointments while they work on the new update. In the meantime, Bethel AME is hosting a vaccine clinic for seniors Sunday, January 7. It's part of the governor's initiative to give access to people in under-served communities.