How do you add custom fields defined in posts to the rest API responses in wordpress

First you need to register_rest_fields to adding custom endpoints in WP REST API JSON Response

add_action( 'rest_api_init', 'add_custom_fields' );
function add_custom_fields() {
register_rest_field(
'post', 
'custom_fields', //New Field Name in JSON RESPONSEs
array(
    'get_callback'    => 'get_custom_fields', // custom function name 
    'update_callback' => null,
    'schema'          => null,
     )
);
}

Then define your functions to get custom fields

function get_custom_fields( $object, $field_name, $request ) {
//your code goes here
return $customfieldvalue;
}

Tested on local site