How to Change Sort Order of default WordPress Catgory Widgets?

@Sandun why don’t you create your own widget?

<?php
class Category_List_Custom extends WP_Widget {

/**
 * Sets up the widgets name etc
 */
public function __construct() {
    $widget_ops = array( 
        'classname' => 'category_list_custom',
        'description' => 'Category list custom',
    );
    parent::__construct( 'category_list_custom', 'Category List Custom', $widget_ops );
}

/**
 * Outputs the content of the widget
 *
 * @param array $args
 * @param array $instance
 */
public function widget( $args, $instance ) {
    $cats = get_categories();
    $ordered_cats = array();
    foreach($cats as $cat){
      $ordered_cats[$cat->category_count] = $cat;
    }
    ksort($ordered_cats);
    $return = '<ul>';
    foreach($ordered_cats as $cat){
      $return .= '<li>' . $cat->name . '</li>';

    }
    $return .= '</ul>';

    return $return;
}

}
add_action( 'widgets_init', function(){
    register_widget( 'Category_List_Custom' );
});?>

It should be something very similar to this.

Let me know if it helps.