In Artifactory, we do have an option to enable/disable the replications globally from the UI by checking/unchecking the checkbox on the replication screen below or we can use the REST API in order block and unblock the complete pull/push replication.
Also, it is possible to enable/disable replication at the repository level as below:
However, the only way to stop a running replication job is to restart the Artifactory instance or cluster. A rolling restart, if it is a HA cluster, would be the best bet for no downtime.
To understand the status of the replication is it Stopped, Running, Inprogress and is it Scheduled task or manual task, we can trigger the Get Background task REST API and verify the status.
And to understand more on replication to print more verbose log in the Artifactory service logs, add the following to the file $JFROG_HOME/artifactory/var/etc/artifactory/logback.xml, before the closing </configuration> tag(No Restart is required).
NOTE: Please enable the logger only for debug purposes and remove it once the relevant information is captured as debug loggers print more logs which may cause performance degradation.