Grab the parent category $category = get_category_by_slug( 'category-name' );
Set whatever args you need for your post query, but make sure to include the child_of
arg
$args = array(
'type' => 'post',
'child_of' => $category->term_id,
'hierarchical' => 1,
'taxonomy' => 'category',
);
Get your subcategories based on these args $child_categories = get_categories($args);
You’ll get an associative array back, which you can loop over using foreach
or whatever iterative function you want. If you want a more detailed solution to a specific problem in terms of a front-end application of this, feel free to update your question or post a comment.