Here is a link to election returns for the Alabama special primaries for U.S. Senate. It appears there will be a run-off primary for the Republicans on September 26, because no one has a majority so far.
The special election itself is not until December 12. The petition deadline for any unqualified party or independent candidate was August 15, and no one submitted a petition. If the state had a reasonable law, the petition would not be due until September 26, the date the major party nominees will be known.