要在Android中使用MQTT WebSocket连接AWS IoT，并使用自定义授权者，可以按照以下步骤进行操作：

1. 首先，确保你已经在Android项目中引入了AWS SDK和MQTT依赖项。

2. 创建一个MqttManager类，该类用于管理MQTT连接和消息。在该类中，你需要初始化AWSIoTClient和AWSIotMqttClient。示例代码如下：

import com.amazonaws.auth.AWSStaticCredentialsProvider;
import com.amazonaws.auth.BasicAWSCredentials;
import com.amazonaws.regions.Region;
import com.amazonaws.regions.Regions;
import com.amazonaws.services.iot.AWSIot;
import com.amazonaws.services.iot.AWSIotClient;
import com.amazonaws.services.iot.model.*;
import com.amazonaws.services.iotdata.AWSIotData;
import com.amazonaws.services.iotdata.AWSIotDataClient;
import com.amazonaws.services.iotdata.model.PublishRequest;

public class MqttManager {
    private AWSIot awsIotClient;
    private AWSIotMqttClient awsIotMqttClient;

    public MqttManager() {
        BasicAWSCredentials credentials = new BasicAWSCredentials("YOUR_ACCESS_KEY", "YOUR_SECRET_KEY");

        awsIotClient = AWSIotClient.builder()
                .withCredentials(new AWSStaticCredentialsProvider(credentials))
                .withRegion(Region.getRegion(Regions.YOUR_REGION))
                .build();

        awsIotMqttClient = new AWSIotMqttClient("YOUR_ENDPOINT", "CLIENT_ID",
                awsIotClient.getCachedEndpointAddress().replaceAll("https://", ""));
    }

    public void connect() {
        awsIotMqttClient.connect();
    }

    public void disconnect() {
        awsIotMqttClient.disconnect();
    }

    public void publish(String topic, String message) {
        PublishRequest publishRequest = new PublishRequest();
        publishRequest.setTopic(topic);
        publishRequest.setPayload(ByteBuffer.wrap(message.getBytes()));

        try {
            AWSIotData awsIotDataClient = new AWSIotDataClient(awsIotClient);
            awsIotDataClient.publish(publishRequest);
        } catch (Exception e) {
            e.printStackTrace();
        }
    }
}

3. 在你的Activity或Fragment中使用MqttManager类。示例代码如下：

public class MainActivity extends AppCompatActivity {
    private MqttManager mqttManager;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);

        mqttManager = new MqttManager();
        mqttManager.connect();

        // 发布消息
        mqttManager.publish("topic", "message");
    }

    @Override
    protected void onDestroy() {
        super.onDestroy();

        mqttManager.disconnect();
    }
}

请确保将以下值替换为你自己的值：

• YOUR_ACCESS_KEY: 你的AWS访问密钥
• YOUR_SECRET_KEY: 你的AWS秘密密钥
• YOUR_REGION: 你的AWS区域
• YOUR_ENDPOINT: 你的AWS IoT端点
• CLIENT_ID: 你的客户端ID

这是一个基本的示例，你可以根据你的需求进行更多的自定义。