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:

WordPress Option Framework