I want to do this without using any sort of plugin since these are both core wordpress features (custom fields and the REST API). Here is the documentation for custom fields
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