public sealed class ServerConnectionProjectItem : ArcGIS.Desktop.Internal.Catalog.ProjectItemInfoCrawl, ArcGIS.Desktop.Core.IMetadata, ArcGIS.Desktop.Core.IProjectItem, ArcGIS.Desktop.Core.IProjectMultiItem, System.ComponentModel.INotifyPropertyChanged  

/// Get all the server connections in a project
IEnumerable<ServerConnectionProjectItem> projectServers = Project.Current.GetItems<ServerConnectionProjectItem>();

IEnumerable<ServerConnectionProjectItem> newServerConnections = null;
newServerConnections = project.GetItems<ServerConnectionProjectItem>();
foreach (var serverItem in newServerConnections)
{
  //Do Something with the server connection.
}

ServerConnectionProjectItem serverProjItem = Project.Current.GetItems<ServerConnectionProjectItem>().FirstOrDefault(item => item.Name.Equals("myServer"));

//This workflow would work for 
      var agsFilePath = @"C:\Data\ServerConnectionFiles\AcmeSampleService.ags";

      //ServerConnectionProjectItem supports .ags, .wms, .wmts, .wfs, and .wcs files
      var server_conn_item = ItemFactory.Instance.Create(agsFilePath) 
  as ArcGIS.Desktop.Catalog.ServerConnectionProjectItem;
      
      //Get the server connection - passwords are never returned
      var serverConnection = server_conn_item.ServerConnection as CIMProjectServerConnection;

//Add to an AGS service connection
var service_connection = new CIMAGSServiceConnection()
{
  URL = "URL to the AGS _service_ on the AGS _server_",
  ServerConnection = serverConnection
};

      // Add a new layer to the map
      var layerParams = new LayerCreationParams(service_connection);
      layerParams.MapMemberPosition = MapMemberPosition.AddToBottom;
      var map = MapView.Active.Map;
      await QueuedTask.Run(() =>
      {
          var layer = LayerFactory.Instance.CreateLayer<FeatureLayer>(layerParams, map);
      });