This plugin for sent information about comment to post author. 
Information about author name and author e-mails sets in custom fields for each post. 
In configuration of plugin you can set keys name for custom fields. By default this is “Author name” and “Author email”. 
Also can set subject and body of notification e-mail. 
In body of e-mail you can use macros:
[name] – name of authr from custom field 
[url] – post url 
[title] – post title 
[comment] – comment text

Comment Inform

This plugin for sent information about comment to post author. Infromation about authors gets from custom fields. Custom fields keys are "Author  …

edik

Extends the <a href="https://wordpress.org/plugins/highfly/" rel="ugc">Highfly plugin</a>. Adds notifications for privately published posts and for comments to private posts and pages.

Highfly Private

Gets Highfly to notify of not only public but also private published content.

Comment Inform vs Highfly Private