To enable publishing Zoho Desk ticket comments as private Jira issue comments, follow these steps:
Make sure that Connection is configured as per Getting Started page
2. Ensure that you are on the latest version of the Jira Extension for Zoho Desk
Navigate to the Jira Extension for Zoho Desk app in the Marketplace. Check if the Update button is visible in the top right corner. If the button is not present, you are already on the latest version. If the button is available, proceed to update to the latest version.
3. Ensure that Auto Sync is enabled
4. Navigate to Jira and enable the options in the Connection Settings
Given the Ticket private comment below
it will be published as an internal comment in Jira.

This section guides you through configuring exactly which Zoho Desk comments are published to Jira. You can control:
Whether Public, Private, or All comments are synced
Whether only comments with specific tags should be published
Navigate to Extension Settings.
Locate the setting: Publish Zoho Desk Comments to Jira Issue
Comment Privacy
You can control which type of Zoho Desk comments are published to Jira.
Publishes both Public and Private comments
Publishes only Public comments
Publishes only Private comments
Select the option that matches your workflow.
Once saved, only the selected comment types will be pushed to the linked Jira issue.
Comment Tag Filter
The Comment Tag Filter allows you to further restrict which comments are published to Jira based on tags included in the comment body.
Only comments containing at least one of the specified tags will be synced.
If no tags are configured, all comments (based on the Privacy setting) will be eligible for syncing.
Locate the Comment Tag Filter field.
Enter a space separated list of tags.
With the example above:
Only comments that contain #jira in the comment body will be synced to Jira.
Comments without this tag will NOT be published.
You may also configure multiple tags:
In this case, any comment containing at least one of these tags will be synced.