try SerializeConfig

SerializeConfig config = new SerializeConfig();

        config.put(Date.class, (serializer, object, fieldName, fieldType, features) -> {
            if (object == null) {
                serializer.out.writeNull();
                return;
            }
            SimpleDateFormat dateFormat = new SimpleDateFormat("yyyy-MM-dd'T'HH:mm:ss.SSS'Z'");
            dateFormat.setTimeZone(TimeZone.getTimeZone("UTC"));
            serializer.out.writeString(dateFormat.format(object));
        });

        String json = JSON.toJSONString(obj, config, SerializerFeature.WriteNonStringValueAsString);