example using Gtk.MenuButton()

gtkmb1

# !/usr/bin/python3
__author__ = 'sam'
from gi.repository import Gtk


class Window(Gtk.Window):
    def __init__(self):
        Gtk.Window.__init__(self)
        self.set_default_size(400, 200)
        self.set_default_geometry(400, 200)

        hb = Gtk.HeaderBar()
        hb.props.show_close_button = True
        hb.props.title = "Click me"
        self.set_titlebar(hb)

        box = Gtk.Box(orientation=Gtk.Orientation.HORIZONTAL)
        pmenu = Gtk.Menu()
        pmenu.append(Gtk.MenuItem(label="lp"))
        pmenu.append(Gtk.MenuItem(label="pl"))
        mb = Gtk.MenuButton()
        mb.set_popup(pmenu)
        box.add(mb)
        hb.pack_end(box)


        self.count = 0;
        self.button = Gtk.Button(label="count")
        self.button.connect('clicked', self.onclick)

        vbox = Gtk.VBox();
        vbox.add(self.button)
        self.add(vbox)


    def onclick(self, widget):
        self.count += 1
        self.button.set_label('Clicked : ' + str(self.count) + ' times')




win = Window()
win.connect("delete-event", Gtk.main_quit)
win.show_all()
Gtk.main()