You can mark any issue in Jira as your personal favorite, just open issue and click star Star icon:
You can use the star Star dropdown to add the issue to a separate favorites list:
The main goal is to use the star as a field which can be added to issue for searching and to different gadgets:
Also, you can use star on the issue search screen, just add Star column to the list and click on the Star icon to mark issue as favorite:
Finally, you can manage your favorites in Jira gadgets: