How to add Jquery Validation to Custom form and set error to field?
If the form field is empty you need to stop propagation of the parent form. This should be what you need.

 countryValidation = function() {
    // Lets use a function so we can check the field
    $country = $('#country');
    if ($country.val() === '') {
      return false;
    } else {
      return true;
    }
  }

  $('#user-number-value').on('focus', function(){
    if(countryValidation() === false){
      // If the field check comes back false on focus lets add a class
      $('#country').addClass('invalid');
    };   
  });

  $('#country').on('change', function(){
    // This will remove the class when the user fixes the error
    if(countryValidation() === true) {
      $('#country').removeClass('invalid'); 
    } else {
      $('#country').addClass('invalid');
    }   
  });

  $('form').on('submit', function(e) {
    if(countryValidation() === false){
      // when the field comes back invalid lets add the class
      $('#country').addClass('invalid');
      // this will prevent the form from submitting
      e.preventDefault();
    }; 
  });