The correct way to override a Wordpress parent theme function in functions.php through a child theme.

WP_OverrideParentThemeFunc.php

<?php

#-----------------------------------------------------------------#
# Example: load revised tinymce file in child theme folder
#-----------------------------------------------------------------#

add_action( 'after_setup_theme', 'new_function_setup' );

function new_function_setup() {
	remove_action('init', 'old_function_init');
	
	function new_function_init() {
		if(is_admin()){
			if(is_edit_page()){
				require_once ( 'child_theme_folder/new_file.php' );		
			}
		}
	}
	
	add_action('init', 'new_function_init');
}


?>