The Epic Link field is a calculated field (i.e. it's not real or stored in the database), it exists purely to allow JQL searches to search for issues linked to a parent issue. The actual link between an Epic and its stories is implemented using an issue link, not a field. There's no way to edit this link directly.
If you're using NextGen web version of Jira, from the backlog tab you can open the Epic panel, Multi-select the Stories you want to add to an epic (Hold down the "CTRL" key and then click on each story in turn) once done, drag the selected items and drop on the desired Epic.
You can use the 'Bulk Edit' option. Select multiple issues in backlog using CTRL or SHIFT, and right click. Select 'Bulk Change' and then select 'Edit Issues'. You can change any number of fields simultaneously, to change the epic select 'Issue Link'.
You will notice there are also other interesting options like move, transition etc.
On October 20, 2021, Atlassian published a security advisory for Jira Service Management. The full advisory is available at this link. We've seen a number of questions already asking for...
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