How To Get WordPress Categories Link List?

Fist error I see is a syntax error:

depth => 0

should be

"depth" => 0

Second error is that you are using a category object like a post object. None of these lines will work:

There is no post data to setup. Remove this line:

setup_postdata($category);

A category object has no category_modified property. Maybe you need the date of the last published post on the category (this is another question)???

//Not valid property
$category->category_modified;

get_permalink() is for posts, for categories use get_category_link() instead. Also, $category->ID is not a valid property of a category object, use $category->term_id instead:

//Incorrect
get_permalink($category->ID);

//Correct
get_category_link($category->term_id);