This guide is based on Recurring Tasks provided by Gebsun Software. Please make sure that Recurring Tasks plugin is installed in your Jira first.

Depending on your needs, the built-in Default Checklist feature might be a better solution to add the checklist automatically to newly created issues.

The guide works for Classic projects only. Next-gen projects are too limited at the moment.

Prerequisites

"Checklist Text" field must be present on the Create Issue screen (current version of Recurring Tasks cannot fill a field that is not present on the "Create Issue" screen).
Please note that you can still hide the field from the Issue View page.
"Save checklist data to Jira custom fields" option must be enabled in Issue Checklist Global Settings.

Guide

When creating recurring task (or editing existing), please find "Checklist Text" field in the Create/Edit dialog and put checklist value into the field as shown on the screenshot below:

Checklist Text custom field uses textual representation of checklist.
Wait for recurring issue to be created automatically (or create it from Recurring Tasks menu) and observe Checklist items present on the issue view screen.