For permissions over specific resources, leave the global permissions empty, and configure a “permission target” for that group.
1. Navigate to the “permissions” tab
2. Create a new permission target.
3. Select the Resources that you want the group to have permissions over.
4. Add the group, and select the scope of permissions you want this group to have. As shown in the following screenshot:
Once all is completed, your group in Artifactory should look like this, varies according to the kind of permissions set: