Hi,
Do you mean adding custom field query arguments to the REST API?
Or do you want to add custom field data to the result title or content fields in the REST API results? That might be actually possible. First, set up the advanced title and content fields, with the custom fields you want to display.
Then when doing the REST API request, you can access these generated titles in the $result->asp_data->title and $result->asp_data->content fields.