Authentication cookie sharing between ASP WebForms and ASP.NET Core MVC app

You can share the cookie between the asp.net application and asp.net core application. The data protection stack allows sharing Katana cookie authentication and ASP.NET Core cookie authentication tickets.

You need add code like below:

public void ConfigureServices(IServiceCollection services)
{
    ...
    services.AddAuthentication();
    ...
}

app.UseCookieAuthentication(new CookieAuthenticationOptions
{
    DataProtectionProvider = DataProtectionProvider.Create(new DirectoryInfo(@"c:\shared-auth-ticket-keys\"))
});

And in your webform application.

app.UseCookieAuthentication(new CookieAuthenticationOptions
{
    AuthenticationType = "Cookies",
    CookieName = ".AspNetCore.Cookies",
    // CookiePath = "...", (if necessary)
    // ...
    TicketDataFormat = new AspNetTicketDataFormat(
        new DataProtectorShim(
            DataProtectionProvider.Create(new DirectoryInfo(@"c:\shared-auth-ticket-keys\"))
            .CreateProtector("Microsoft.AspNetCore.Authentication.Cookies.CookieAuthenticationMiddleware",
            "Cookies", "v2")))
});

For more details you can check the link I provided.

And you also can find the refer the webform repo.