There is no such function that allows you to clone the epic and linked issues. I found this feature request, JSWSERVER-7721, and one of the comments mention a workaround were they use the export/import functionality. The app mentioned only works on Server and I could not find one that works in Cloud.
For Jira cloud we released a Marketplace app called Deep Clone for Jira that enables you to clone Epics and all included tasks and subtasks in one action.
If you have any questions, feedback or feature requests don't hesitate to contact us at email@example.com.
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