How can I read WPF publish version number in code behind

Use GetEntryAssembly rather than GetExecutingAssembly to get the version from the current executable rather than from the currently-executing DLL, like so:

string version = System.Reflection.Assembly.GetEntryAssembly().GetName().Version.ToString();

Add reference to System.Deployment library to your project and adjust this snippet to your code:

using System.Deployment.Application;

and

string version = null;
try
{   
    //// get deployment version
    version = ApplicationDeployment.CurrentDeployment.CurrentVersion.ToString();
}
catch (InvalidDeploymentException)
{
    //// you cannot read publish version when app isn't installed 
    //// (e.g. during debug)
    version = "not installed";
}

As stated in comment, you cannot obtain publish version during debug, so I suggest to handle InvalidDeploymentException.

Access the assembly version using Assembly.GetExecutingAssembly() and display in UI

Assembly.GetExecutingAssembly().GetName().Version.ToString();