Add custom input field via action hooks.
Code Sample:
add_action('wp_theme_settings_field_hello_world','wp_theme_settings_field_hello');
function wp_theme_settings_field_hello($option){
$id = isset( $option['id'] ) ? $option['id'] : "";
$args = isset( $option['args'] ) ? $option['args'] : "";
?>
<div class="">Hello World!</div>
<?php
var_dump($args);
}
array(
'id' => 'custom_field_hello',
'title' => __('Custom field hello world','text-domain'),
'details' => __('Description of custom input field hello world','text-domain'),
'type' => 'hello_world',
'args' => array(
'option_1' => __('Option 1','text-domain'),
'option_2' => __('Option 2','text-domain'),
'option_3' => __('Option 3','text-domain'),
'option_4' => __('Option 4','text-domain'),
),
),
Preview:

