You can use Jira REST API to work with the checklists.
You can read/write checklists by using Jira REST API accessing a “Checklists” custom field.
Read more about custom fields used by Smart Checklist addon and their setup here: https://railsware.atlassian.net/wiki/spaces/CHKSDC/pages/2349925102/Custom+Fields
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
Since Smart Checklist version 5.0.0 we’ve deprecating com.railsware.SmartChecklist.checklist issue property as the main checklist storage.
Read more here https://railsware.atlassian.net/wiki/spaces/CHKSDC/pages/2046623745
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/Formatting+Guide 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.