You can use Jira REST API to work with the checklists.
Now the Smart Checklist dedicated REST API is available! For more complex use cases and integrations - follow the instructions https://railsware.atlassian.net/wiki/spaces/CHKSDC/pages/3238854657
You can read/write checklists by using Jira REST API accessing a Checklists custom field or com.railsware.SmartChecklist.checklist issue property
Read more about custom fields used by Smart Checklist addon and their setup here: https://railsware.atlassian.net/wiki/spaces/CHKSDC/pages/2349925102
Get checklist value rom existing Jira issue
Use the Get Issue Jira REST API
Create Jira issue with the checklist applied
Use the Create Issue Jira REST API
Set the checklist for existing Jira issue
Use the Edit Issue Jira REST API
Jira REST API
Jira REST API examples
Use checklist RAW text Markdown format to set its value. Check the https://railsware.atlassian.net/wiki/spaces/CHKSDC/pages/2316861534 for more info.
"customfield_10001": "- ToDo List\n+ Checked\nx Skipped\n~ In Progress\n# Another ToDo List\n- Unchecked\n> Quote line 1 https://rw.rw\\n> Quote line 2\n> Quote line 3\n"
Custom field id customfield_10001 might be different on your instance. Make sure you use the correct one.
Here’s How to find id for custom field “Checklist” on Jira Server and Data Center.