The parent folder should be marked as "Orderable" in the properties.This changes the JCR type of the folder to "sling:OrderedFolder", which in turn supports ordering for the children.

I have a custom component that relies on JCR order for displaying assets (specifically, Content Fragments) in a particular order. The order should be customizable by Authors.In AEM 6.5.6 and prior, the assets could be ordered in the List View by drag and dropping a handle at the right hand side of t...

Not really; When a page that references the HTL component is rolled out, nothing happens to the actual component template. It exists in a single instance.You can write a custom Sling Rewriter to do that on page render time.