Add menu option to favoured app launcher in Ubuntu dock

Follow the steps below.

1. Copy .desktop file associated to your preferred application, say app-name.desktop from /usr/share/applications/ to ~/.local/share/applications/. You can do this by running the following command in Terminal

   cp /usr/share/applications/app-name.desktop ~/.local/share/applications/
   

2. Open the .desktop file using a text-editor, for example by running

   gedit ~/.local/share/applications/app-name.desktop
   

3. Look for a line beginning with Actions=. If there is one, append My-Custom-Action; to it. Otherwise, add the following line

   Actions=My-Custom-Action;
   

4. Write the following lines at end of the file:

   [Desktop Action My-Custom-Action]
   Name=Name of the Option
   Exec=command-you-want-to-run
   

   For example, if you want to open Text editor, put gedit in place of command-you-want-ro-run.

5. Save the file.

6. Click on "Activities" and search for the application.

7. Right-click on the application icon and select "Add to Favourites". It should be added to the Ubuntu dock.

Now if you right-click on the newly added application icon in the dock, you should see a "Name of the Option" entry in the context menu which should work as expected.

Similarly, you can other options by adding new Desktop Actions and adding the name of the action to the Actions= line. For more info see this.