This code would be added in your child theme's functions.php and what it does is re-registeres the child theme with the current style.css version number so whenever you make changes to your child theme you can update your version number and it will update the ?v= parameter in the style.css URL to prevent browser caching.
add_action( 'wp_enqueue_scripts', function() {
if ( ! defined( 'WPEX_THEME_STYLE_HANDLE' ) ) {
return;
}
// First de-register the main child theme stylesheet
wp_deregister_style( WPEX_THEME_STYLE_HANDLE );
// Then add it again, using filemtime for the version number so everytime the child theme changes so will the version number
wp_register_style( WPEX_THEME_STYLE_HANDLE, get_stylesheet_uri(), array(), filemtime( get_stylesheet_directory() . '/style.css' ) );
// Finally enqueue it again
wp_enqueue_style( WPEX_THEME_STYLE_HANDLE );
} );