public override Geodatabase Connect()

{
  // Must be called within QueuedTask.Run
  Geodatabase ConnectToVersion(Geodatabase geodatabase, string versionName)
  {
    Geodatabase connectedVersion = null;

    if (geodatabase.IsVersioningSupported())
    {
      using (VersionManager versionManager = geodatabase.GetVersionManager())
      using (Version version = versionManager.GetVersion(versionName))
      {
        connectedVersion = version.Connect();
      }
    }

    return connectedVersion;
  }
}

{
  await QueuedTask.Run(() =>
  {
    using (Geodatabase geodatabase = new Geodatabase(new DatabaseConnectionFile(new Uri("path\\to\\sde\\file"))))
    using (VersionManager versionManager = geodatabase.GetVersionManager())
    {
      IReadOnlyList<string> versionNames = versionManager.GetVersionNames();

      Version defaultVersion = versionManager.GetDefaultVersion();

      string testVersionName = versionNames.First(v => v.Contains("Test"));
      Version testVersion = versionManager.GetVersion(testVersionName);

      Version qaVersion = defaultVersion.GetChildren().First(version => version.GetName().Contains("QA"));

      Geodatabase qaVersionGeodatabase = qaVersion.Connect();

      FeatureClass currentFeatureClass = geodatabase.OpenDataset<FeatureClass>("featureClassName");
      FeatureClass qaFeatureClass = qaVersionGeodatabase.OpenDataset<FeatureClass>("featureClassName");
    }
  });
}