Problem retriving the post type category

get_terms retrieves all terms in a taxonomy, not terms added to a post.

you want to use get_the_terms to retrieve terms assigned to a specific post. there are no additional arguments to filter the list of terms returned, you’ll have to manually check a term’s parent to only output terms that are a child of a specific term id.

$terms = get_the_terms( $post->ID, 'seriale' );
foreach( $terms as $term ):
    if( 668 == $term->parent ){
        echo $term->name;
    }
endforeach;