AspNetCore alternative for System.Web.Security.FormsAuthenticationTicket

Asp.net core cannot support form authentication. I recommend you use cookie-base authentication. This link can help you build it.

If you want to skip a method that requires authorized access. You can add attribute [AllowAnonymous].

    [AllowAnonymous]
    public IActionResult Privacy()
    {
        return View();
    }

Or you can refer to this link.

Configure cookie in Startup.cs.

services.AddAuthentication("auth")
            .AddCookie("auth",config=>
            {
                config.Cookie.Name = "cookie.name";
                config.LoginPath = "/home/login";
            });

Generate token in this action. You can fill the claim by receiving form data.

[HttpPost]
public IActionResult login()
    {
        var claims = new List<Claim>
        {
            new Claim(ClaimTypes.Name,"myName"),
            new Claim(ClaimTypes.Role,"myRole")
        };
        var claimIdentity = new ClaimsIdentity(claims,"id card");
        var claimPrinciple = new ClaimsPrincipal(claimIdentity);
        var authenticationProperty = new AuthenticationProperties
        {
            IsPersistent = true
        };
        HttpContext.SignInAsync(claimPrinciple,authenticationProperty);
        
        return View();
    }