Задача таймера с приоритетным сервисом

Вы можете сделать это с помощью BroadcastReceiver.

вот некоторые настройки, использующие BroadcastReceiver.

<manifest xmlns:android = "http://schemas.android.com/apk/res/android"
    package = "com.example.myapp">

    <application
        android:allowBackup = "true"
        android:icon = "@mipmap/ic_launcher"
        android:label = "@string/app_name"
        android:roundIcon = "@mipmap/ic_launcher_round"
        android:supportsRtl = "true"
        android:theme = "@style/AppTheme">
        <!-- Other components -->

        <receiver
            android:name = ".ScreenStateReceiver"
            android:enabled = "true"
            android:exported = "true">
            <intent-filter>
                <action android:name = "android.intent.action.SCREEN_OFF" />
                <action android:name = "android.intent.action.SCREEN_ON" />
            </intent-filter>
        </receiver>
    </application>

</manifest>

Добавьте это разрешение в манифест

<uses-permission android:name = "android.permission.RECEIVE_BOOT_COMPLETED" />

Файл ScreenStateReceiver.java

public class ScreenStateReceiver extends BroadcastReceiver {
    @Override
    public void onReceive(Context context, Intent intent) {
        if (Intent.ACTION_SCREEN_OFF.equals(intent.getAction())) {
            MainActivity.stopTimerTask();
        } else if (Intent.ACTION_SCREEN_ON.equals(intent.getAction())) {
            MainActivity.startTimerTaskIfNecessary();
        }
    }
}

// In your MainActivity
public static void startTimerTaskIfNecessary() {
    if (timer == null) {
        timer = new Timer();
        // Schedule your task here
    }
}

public static void stopTimerTask() {
    if (timer != null) {
        timer.cancel();
        timer.purge();
        timer = null;
    }
}

MainActivity.java

public class MainActivity extends AppCompatActivity {
    private ScreenStateReceiver screenStateReceiver;

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

    }

    @Override
    protected void onResume() {
        super.onResume();
        if (screenStateReceiver == null) {
            screenStateReceiver = new ScreenStateReceiver();
            IntentFilter filter = new IntentFilter();
            filter.addAction(Intent.ACTION_SCREEN_OFF);
            filter.addAction(Intent.ACTION_SCREEN_ON);
            registerReceiver(screenStateReceiver, filter);
        }
    }

    @Override
    protected void onPause() {
        super.onPause();
        if (screenStateReceiver != null) {
            unregisterReceiver(screenStateReceiver);
            screenStateReceiver = null;
        }
    }
}