AWS API Gateway Custom Domain breaks Authorisation JSWT

I use AWS API Gateway and call it form an Web-App (just jQuery, no Frameworks).

When I call it from code like this, it works:

const sBaseURLNotify= 'https://<my-id>.execute-api.eu-west-1.amazonaws.com/STAGE_default';

$.ajax({
        method: 'PUT',
        crossDomain: true,
        contentType: 'application/json',
        url: this.sBaseURLNotify+'/register_notfication',
        headers: {
          'Authorization': featureLogin.oUser.AccessToken
        },
        data: JSON.stringify({
          oSubscription: JSON.stringify(oSubscription),
        }),
        success: function(data, status) {
          console.log('data', data);
        },
        error: function(xhr, ajaxOptions, thrownError) {
          console.log('thrownError:', thrownError);
          sessionStorage.setItem('oSubscription9', 'none');
          sessionStorage.setItem('iSubscriptiondate', Date.now());
        },
      });

When I instead use the Custom Domain name I set up, it throws the error “Unauthorized”

I just exschange the first line to

const sBaseURLNotify= 'https://stage-api.<my domain name>.de/notification';

The URL seems to be correct, as the Error changes to “”, when I bring in a typo,

const sBaseURLNotify= 'https://stage-api.<my domain name>.de/ntification';

I assume anything in the Custom Domain messes with the “Authorization” header. But I can’t figure out what happens or what I can do about it.

Any suggestions are very welcome!