I am trying to create a button with drop down menu in quick access toolbar like a button whose name is open and in it's drop down menu option will be .prt, .asm, .drw.
Create your group Cascade on the ribbon then go to the Quick Access Toolbar definition and you should see your group or cascade which you can add to it.
The Quick Access Toolbar doesn't have the commands to create the groups or drop down menus. To create those you need to do it in the Customize Ribbon Dialog.
Add a new tab or group, if you add a tab it automatically adds a group. The drop down list you show is what is referred to as a Cascade. Add a Cascade under the group, rename it, and add your mapkeys to it.
Go to the Customize Quick Access Toolbar and you should find the menu you created which can be added to the toolbar.
You can then go back and remove the group from the Ribbon if you don't want it shown there.