I've declared a Service class:
public class MyService extends Service{
 @Nullable
 @Override
 public IBinder onBind(Intent intent) {
     return null;
 }
 @Override
 public int onStartCommand(Intent intent, int flags, int startId) {
     new Parsing().execute();
     return Service.START_STICKY;
}
private class Parsing extends AsyncTask<Void, Void, Void> {
    List<MyObject> myList = null;
    MyAdapter adapter = null;
    @Override
    protected void onPreExecute() {
        super.onPreExecute();
        myList = new ArrayList<MyObject>();
    }
    @Override
    protected Void doInBackground(Void... params) {
        while (downloadDataFromInternet)
            myList.add(new MyObject(par1, par2, par3, par4));
    }
    @Override
    protected void onPostExecute(Void result) {
        if (myList.size() > 0) 
            adapter = new MyAdapter(this, myList);
    }
}
}
Now I would like to execute this service every 10 minutes (for example) also when activity is in background, but I want that when activity come back to foreground, listView of MyFragment uses the adapter declared in the service. Can you please help me? I have no idea about how to do this.
                        
You can use Timer Task to execute some task after a specific time period
1 You need to create Subclass of TimerTask
eg
2 Start this task from your service
Hope this is what you want