Abidemi Kusimo

You can make use of category popular tag to display most used tag on your blog. This will give list of frequently used tag anywhere you place the shortcode or funtion in your theme.
For example [popular_category_tags count=10 type=”popular-tags” category_id=”1″]. 
You can also call this function from your theme file: cush_category_popular_tag() for basic output.
When using the shortcode type is required. category id, count is not required. if no category id suplied, the plugin will default to current post category available. 
For example [popular_category_tags type=”popular-tags” ].
You can find category tags options under Settings page 
Settings -> Category Tags
Credit : (https://wordpress.stackexchange.com/questions/261617/display-most-popular-tags-of-category)

Category Popular Tags

Display popular tags on achieve/category page of your theme using sortcode or by calling a function.

Nader

The “Most Comments” plugin displays as the name says posts with the most comments. You can either use the widget in the sidebar or integrate the plugin as template tag in your theme files.
Features:
<ul>
<li>Limit the amount of posts to be shown</li>
<li>Show comments from a specific post category</li>
<li>Exlude posts without comments</li>
<li>Select a time range (last XX days) of posts to be taken into account</li>
<li>Customize the design template via the settings page</li>
<li>Place a widget in your sidebar</li>
</ul>
More Information & Feature Description: 
http://www.brandinfection.com/wordpress-plugins/most-comments/
<h3>Configuration</h3>
You can configure the most comments plugin to your needs. Options can be found under the menu <code>Settings > Most Comments</code>

Most Comments

Display posts with the most comments, as a widget or on a page using the template tag. Customize the look with specific settings.

Category Popular Tags vs Most Comments