No authenticationScheme was specified, and there was no DefaultChallengeScheme found with default authentification and custom authorization

Do not use authorization instead of authentication. I should get whole access to service all clients with header.

The working code is:

public class TokenAuthenticationHandler : AuthenticationHandler<TokenAuthenticationOptions> 
{
    public IServiceProvider ServiceProvider { get; set; }

    public TokenAuthenticationHandler (IOptionsMonitor<TokenAuthenticationOptions> options, ILoggerFactory logger, UrlEncoder encoder, ISystemClock clock, IServiceProvider serviceProvider) 
        : base (options, logger, encoder, clock) 
    {
        ServiceProvider = serviceProvider;
    }

    protected override Task<AuthenticateResult> HandleAuthenticateAsync () 
    {
        var headers = Request.Headers;
        var token = "X-Auth-Token".GetHeaderOrCookieValue (Request);

        if (string.IsNullOrEmpty (token)) {
            return Task.FromResult (AuthenticateResult.Fail ("Token is null"));
        }           

        bool isValidToken = false; // check token here

        if (!isValidToken) {
            return Task.FromResult (AuthenticateResult.Fail ($"Balancer not authorize token : for token={token}"));
        }

        var claims = new [] { new Claim ("token", token) };
        var identity = new ClaimsIdentity (claims, nameof (TokenAuthenticationHandler));
        var ticket = new AuthenticationTicket (new ClaimsPrincipal (identity), this.Scheme.Name);
        return Task.FromResult (AuthenticateResult.Success (ticket));
    }
}

Startup.cs:

#region Authentication
services.AddAuthentication (o => {
    o.DefaultScheme = SchemesNamesConst.TokenAuthenticationDefaultScheme;
})
.AddScheme<TokenAuthenticationOptions, TokenAuthenticationHandler> (SchemesNamesConst.TokenAuthenticationDefaultScheme, o => { });
#endregion

And mycontroller.cs:

[Authorize(AuthenticationSchemes = SchemesNamesConst.TokenAuthenticationDefaultScheme)]
public class MainController : BaseController
{ ... }

I can’t find TokenAuthenticationOptions now, but it was empty. I found the same class PhoneNumberAuthenticationOptions:

public class PhoneNumberAuthenticationOptions : AuthenticationSchemeOptions
{
    public Regex PhoneMask { get; set; }// = new Regex("7\\d{10}");
}

You should define static class SchemesNamesConst. Something like:

public static class SchemesNamesConst
{
    public const string TokenAuthenticationDefaultScheme = "TokenAuthenticationScheme";
}