Limit Scheduled Process access to only Custom ESS job

Summary:

We have created a custom ess job that runs a BI report. The privilege created along with the custom job has already been added to the custom role and our user account can already access and run the job.

However, the job result always throws an error after being triggered.

Adding the Manage Scheduled Job Definition privilege on the custom roles under Function Security Policy resolves the issue, however this enables the user account access to other ESS jobs.

Is there any other privilege that we can add to just keep the custom ess job run successfully without enabling it to other ess jobs?