Custom Backend data for map to JSON file?

Use the JSON REST API – http://v2.wp-api.org – It lives as a plugin now but will eventually be part of WP Core – https://wordpress.org/plugins/rest-api/

To manually output JSON, use a combination of wp-ajax to handle requests and wp_json_encode() / wp_send_json_success for simple PHP Objects and Arrays. See https://codex.wordpress.org/AJAX_in_Plugins

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