Exclude category in widget through child theme

Try using WordPress’ built-in filter for widget display called widget_categories_args. You can add a filter function to your child theme’s functions.php that modifies the arguments passed to the wp_list_categories() function, which is what the Categories widget uses (if that’s what the widget you’re trying to modify) to pull its list of categories. Here’s an example:

function filter_widget_categories_args($args) {
    $args['exclude'] = array(10); // ID of the category to exclude
    return $args;
}
add_filter('widget_categories_args', 'filter_widget_categories_args');

The function filter_widget_categories_args will modify the original $args array by adding an exclude key.