public BarItemLinkCollection ItemLinks { get; }

Public ReadOnly Property ItemLinks As BarItemLinkCollection

using DevExpress.XtraBars;
using DevExpress.XtraBars.Ribbon;
using DevExpress.XtraPdfViewer;
using System.Windows.Forms;
//...

void pdfViewer1_PopupMenuShowing(object sender, PdfPopupMenuShowingEventArgs e) {

    // Create a bar button item.
    BarButtonItem browseBarButton = new BarButtonItem();
    browseBarButton.Caption = "Custom Item";

    // Insert the bar button item 
    // and start a new group.
    e.ItemLinks.Add(browseBarButton, true);

    // Handle the bar button click event.
    browseBarButton.ItemClick += browseBarButton_ItemClick;
}

void browseBarButton_ItemClick(object sender, ItemClickEventArgs e) {
    MessageBox.Show("ItemClick event fires");
}

Imports System.Windows.Forms
Imports DevExpress.XtraPdfViewer
Imports DevExpress.XtraBars

'...
Private Sub pdfViewer1_PopupMenuShowing(ByVal sender As Object, ByVal e As PdfPopupMenuShowingEventArgs) Handles pdfViewer1.PopupMenuShowing
    ' Create a bar button item.
    Dim browseBarButton As New BarButtonItem()
    browseBarButton.Caption = "Custom Item"

    ' Insert the bar button item into the PDF Viewer popup menu and start a new group.
    e.ItemLinks.Add(browseBarButton, True)

    ' Handle the bar button click event.
    AddHandler browseBarButton.ItemClick, AddressOf browseBarButton_ItemClick
End Sub

Private Sub browseBarButton_ItemClick(ByVal sender As Object, ByVal e As ItemClickEventArgs)
    MessageBox.Show("ItemClick event fires")
End Sub