by Sajjad Hossain Sagor on WordPress.org
Add Custom Image To Your Category / Custom Taxonomy Field With Advanced Category and Custom Taxonomy Image Plugin.

Settings page for enabling taxonomy image upload for different taxonomies
Now its easier to include category / custom taxonomy image with this plugin for different platforms. No need to overload mobile bandwidth with high pixel image size. You can now select different image for different devices. Upload Different Image For Different Devices ex: Mobile, Tablet, Desktop, iOS, Android, Windows Phone.
Built-in Template Tag To Use Anywhere You Want In Your Theme : get_taxonomy_image( $term_id, $return_img_tag, $class );
$taxonomy_img = get_taxonomy_image( int $term_id = get_queried_object()->term_id , boolean $return_img_tag = false , string $class = '' ); get taxonomy image url if $return_html = true then return tag Parameters : $term_id (int) (Required) Taxonomy ID of the term. $return_img_tag (boolean) (Optional) Formatted Image with tag for the field during output. $class (string) (Optional) A space separated string of CSS classes to add to the tag. classes ex: "your custom class list separated by space" but $return_img_tag should be true to add image class. echo $taxonomy_img; // taxonomy image url
where $term_id is ‘category / term id’
Shortcode : use the shortcode anywhere to get taxonomy image. If you don’t provide “term_id” value then it will be current queried page taxonomy automatically.
echo do_shortcode( '[ad_tax_image term_id="" return_img_tag="true" class="your custom class list seperated by space"]' ); // keep term_id empty if you want to show current visited taxonomy archive image.