Code that is specific to a child-theme page template should be placed in that page template file. (The permitted exception is home.php, for no other reason than that’s what we’ve got used to).
Additional settings screens or option boxes should go in a childthemename-theme-settings.php file.
Additional Editor metaboxes (post/page editor etc) should go in a childthemename-inpost-metaboxes.php file
Script and Additional CSS
Script and additional CSS should be loaded via functions.php