Make Wordpress subcategories use Category Template

One way to do this is to hook into the template_redirect action in your functions.php file:

function myTemplateSelect() {    if (is_category() && !is_feed()) {        if (is_category(get_cat_id('projects')) || cat_is_ancestor_of(get_cat_id('projects'), get_query_var('cat'))) {            load_template(TEMPLATEPATH . '/category-projects.php');            exit;        }    }}add_action('template_redirect', 'myTemplateSelect');

Richard's answer does work but it will heavily interfere with other plugins.

I found a better alternative using add_filter & template_include as the example below

add_filter( 'template_include', 'my_callback' );function my_callback( $original_template ) {    if ( some_condition() ) {        return SOME_PATH . '/some-custom-file.php';    } else {        return $original_template;    }}

Credit to https://markjaquith.wordpress.com/2014/02/19/template_redirect-is-not-for-loading-templates/

As far i know; according to wp template hierarchy, category-samplecat.php is only applies to a category with slug name "samplecat". So it's not possible to do it in this way.

But in the category.php file (that applies to every category which hasn't a special template file) you can make a conditional check if current category is a child of "project" (using this method in my answer to your other question) and if so you can apply same structure of category-projects.php to it or include category-projects.php.