In WooCommerce the rest api is used to get data from orders , products , customers..
but how you can customize or add add other api route  to get (fields and value) , ok it's exist many techniques
first work directly on the core for example inside :

woocommerce/includes/class-wc-api.php in fuction includes or handle_v1_rest_api_request() or handle_v2_rest_api_request() :

add :

 
include_once( 'api/class-wc-api-customs.php' );
 

and you will find apply_filters add you custom class to filters :

 
$api_classes = apply_filters( 'woocommerce_api_classes',
array(
'WC_API_Customers',
'WC_API_Orders',
'WC_API_Customs',
'WC_API_Products',
'WC_API_Coupons',
'WC_API_Reports',
)
);
 

Now you should add the class class-wc-api-customs.php extends WC_API_Resource the content is :

 
<?php
if ( ! defined( 'ABSPATH' ) ) {
exit; // Exit if accessed directly
}
class WC_API_ Customs extends WC_API_Resource {
/** @var string $base the route base */
protected $base = '/customs';
/** @var string $post_type the custom post type */
protected $post_type = 'shop_cart';
/**
* @return array
*/
public function register_routes( $routes ) {
# GET|POST /carts
$routes[ $this->base ] = array(
array( array( $this, 'get_count_customs' ), WC_API_Server::READABLE ),
);
return $routes;
}
public function get_count_customs( $status = null, $filter = array() ) {
$count_customs = 7;
return apply_filters('carts_count',$count_customs);
}
}
 

Conclusion  : we have declared our custom route inside register_routes with name get_count_customs and we created function for done something .
Now you can use by example Api v2 or 3 for call :
wc-api/v3/get_count_customs
2 : plugin :

inside woocommerce-ac.php add :

 
add_action('woocommerce_api_loaded', 'wpc_register_wp_api_endpoints');
function wpc_register_wp_api_endpoints() {
include_once( 'woo-includes/api/v2/class-wc-api-carts.php' );
add_filter('woocommerce_api_classes', 'filter_woocommerce_api_classes', 10, 1);
}
function filter_woocommerce_api_classes($array) {
$cart = array(
'WC_API_Carts',
);
return array_merge($array, $cart);
}
 

and inside woo-includes/api/v2 add class-wc-api-customs.php add you code
that is done