Here is your solution-
<?php
/**
* The template for displaying category archive pages.
*
* @link https://codex.wordpress.org/Template_Hierarchy
*
* @package Codilight_Lite
*/
$cat = get_category( get_query_var( 'cat' ) );
$cat_id = $cat->cat_ID;
$child_categories=get_categories(
array(
'parent' => $cat_id,
// Uncomment the below line if you want empty category to appear on the list.
// 'hide_empty' => 0
)
);
get_header(); ?>
<div id="content" class="site-content container">
<div class="content-inside">
<div id="primary" class="content-area">
<main id="main" class="site-main" role="main">
<?php
foreach ( $child_categories as $child ) { ?>
<article>
<div class="category thumbnail">
<a href="" title=""><img alt="" src="" />
</a>
</div>
<div class="category-title">
<h2 class="entry-title"><?php echo $child ->cat_name;?></h2>
</header><!-- .entry-header -->
<div class="category description">
<?php echo $child ->description;?>
</div><!-- .entry-content -->
</div>
</article>
<?php
}
?>
</main><!-- #main -->
</div><!-- #primary -->
<?php get_sidebar(); ?>
<?php get_footer(); ?>
Just copy and paste it to your archive.php
and you are ready to go. Hope this is gonna help you.