public VersionAccessType GetAccessType()

public async Task WorkingWithVersions()
{
  await ArcGIS.Desktop.Framework.Threading.Tasks.QueuedTask.Run(() =>
  {
    using (Geodatabase geodatabase = new Geodatabase(new DatabaseConnectionFile(new Uri("path\\to\\sde\\file"))))
    using (VersionManager versionManager = geodatabase.GetVersionManager())
    {
      IReadOnlyList<Version> versionList = versionManager.GetVersions();

      Version defaultVersion = versionManager.GetDefaultVersion();

      IEnumerable<Version> publicVersions = versionList.Where(
        version => version.GetAccessType() == VersionAccessType.Public);
      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");
    }
  });
}