Search and JQL support
Not available in next-gen projects. Please see the details here.
To use this functionality you need to set-up "Checklists" custom field, or "Smart Checklist Progress". It depends on what main criteria you'd like to search for.
Smart Checklist supports JQL as an approach for searching checklist items values and checklist progress.
If you set up "Checklists" (multi-line text field) and "Smart Checklist Progress" (single-line text field) which are both custom fields - you can easily apply all JQL search patterns.
You can use Assignee search w/o needs of setting up "Checklists" custom field! Check Search for checklist by assignees article
Search examples
To search for issues with opened checklists (not all checklist items completed).
Type in JQL: "Smart Checklist Progress" ~ "-Done"
To search for issues with ALL completed checklists
Type in JQL: "Smart Checklist Progress" ~ "Done"
To search for all issues that contain checklists on your instance:
Type in in JQL: "Checklists" (or cf[CustomFieldID]) is not EMPTY
To search for checklists containing specific items:
Type in in JQL: "Checklists" (or cf[CustomFieldID]) ~ "your item value":
NB! At this moment, searching for Jira issues where a specific checklist item has completed/ incompleted status is unavailable. This happens due to the following limitation: Jira does not index the special character of - and +
Source: https://confluence.atlassian.com/jirasoftwareserver0712/search-syntax-for-text-fields-959315338.html