Not Showing Image on category page

Hi there,

are you using this plugin?
https://pe.wordpress.org/plugins/categories-images/

As your hook settings look correct it would mean the z_category function is not being called. Which would mean there is an issue with the plugin... as its really out of date theres not much we can do troubleshoot the issue.

I didn't install any plugin for showing category images.

That function you're using requires that Plugin to be installed. It provides the Images field in your Post > Categories and generates the output on the front end.