Question

The question is in the title but to make it clearer when you use a normal server control like

<asp:textbox /> 
<CC1:CtrlArticleList SortBy="Title"  ID="compositeControlArticleList" runat="server" />

the properties of textbox allow you to select from a dropdown list (eg visibility=…true or false). How do I replicate this in composite control?

Added code since question asked:

Someone suggested using an enum but not sure how to set this up:

enum SortBY { Date, Title };

        [Bindable(false), DefaultValue(""), Description("The sorting type of the DataPager")]
    public SortBY SortBySomething
    {
        get
        {
            SortBY getDate = SortBY.Date;
            if(getDate == (SortBY)ViewState["SortBy"])
            {
                return SortBY.Date;
            }
            else
            {
                return SortBY.Title;
            }
        }
        set 
        { 
            ViewState["SortBy"] = value; 
        }
    }

Answer 1

Just make them properties in your composite control like the example from MSDN below. Your public properties will then show up in the intellisence. If they don;t you may need to rebuild you app first.

 public class Register : CompositeControl
{
    private Button submitButton;

    // The following properties are delegated to 
    // child controls.
    [
    Bindable(true),
    Category("Appearance"),
    DefaultValue(""),
    Description("The text to display on the button.")
    ]
    public string ButtonText
    {
        get
        {
            EnsureChildControls();
            return submitButton.Text;
        }
        set
        {
            EnsureChildControls();
            submitButton.Text = value;
        }
    }

After seeing your comment I think what you are looking for is (may not be perfect didn;t test but its close):

public enum SortType{Name,Date}    

public SortType SortBy 
{
    get{
           if(ViewState["SortBy"] != null){
              return (SortType)ViewState["SortBy"];}
           else{return SortType.Date;}
    }
    set{ViewState["SortBy"] = value;}
}