activity_main.xml
<?xml version="1.0" encoding="utf-8"?>
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:tools="http://schemas.android.com/tools"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:gravity="center"
    android:orientation="vertical"
    tools:context="com.androidsimplifycodes.example.MainActivity">
    <Button
        android:id="@+id/btnPopUpMenu"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:text="Popup Menu"
        android:textColor="@android:color/black"
        android:textStyle="bold" />
</LinearLayout>
    For the icons right click on drawable folder and select New->Vector Asset then after added required icons.
    pop_up_menu.xml
<?xml version="1.0" encoding="utf-8"?>
<menu xmlns:android="http://schemas.android.com/apk/res/android">
    <item
        android:id="@+id/action_phone"
        android:icon="@drawable/ic_call"
        android:title="Phone" />
    <item
        android:id="@+id/action_mail"
        android:icon="@drawable/ic_post"
        android:title="Mail" />
    <item
        android:id="@+id/action_add_to_calender"
        android:icon="@drawable/ic_calendar"
        android:title="Calender" />
</menu>
    MainActivity.java
package com.androidsimplifycodes.example;
import android.content.Context;
import android.os.Bundle;
import android.support.v7.app.AppCompatActivity;
import android.support.v7.view.menu.MenuBuilder;
import android.support.v7.view.menu.MenuPopupHelper;
import android.support.v7.widget.PopupMenu;
import android.view.MenuItem;
import android.view.View;
import android.widget.Button;
import android.widget.Toast;
public class MainActivity extends AppCompatActivity {
    protected Context context;
    protected Button btnPopUpMenu;
    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        super.setContentView(R.layout.activity_main);
        context = MainActivity.this;
        initView();
        btnPopUpMenu.setOnClickListener(new View.OnClickListener() {
            @Override
            public void onClick(View view) {
                PopupMenu popupMenu = new PopupMenu(context, view);
                popupMenu.getMenuInflater().inflate(R.menu.pop_up_menu, popupMenu.getMenu());
                popupMenu.setOnMenuItemClickListener(new PopupMenu.OnMenuItemClickListener() {
                    public boolean onMenuItemClick(MenuItem item) {
                        switch (item.getItemId()) {
                            case R.id.action_mail:
                                Toast.makeText(context, item.getTitle(), Toast.LENGTH_SHORT).show();
                                break;
                            case R.id.action_phone:
                                Toast.makeText(context, item.getTitle(), Toast.LENGTH_SHORT).show();
                                break;
                            case R.id.action_add_to_calender:
                                Toast.makeText(context, item.getTitle(), Toast.LENGTH_SHORT).show();
                                break;
                        }
                        return true;
                    }
                });
                MenuPopupHelper menuHelper = new MenuPopupHelper(context, (MenuBuilder) popupMenu.getMenu(), view);
                menuHelper.setForceShowIcon(true);
                menuHelper.show();
            }
        });
    }
    private void initView() {
        btnPopUpMenu = (Button) findViewById(R.id.btnPopUpMenu);
    }
}
    Output : 









