Form data is not being sent with the ajax request. Make sure to utilize $('#myform').serialize() for sending the data.

Furthermore, ensure that the <select> tag has a name attribute included in it.

The correct format for the

<select id="select" class="form-control" name="client">

Follow this example:

$(document).ready(function(){
   $('#submit').click(function(event){
       event.preventDefault();
       $.ajax({
          url : "<?= base_url('Invoice/invoiceData') ?>",
          method : 'POST',
          data: $('#myform').serialize(),
          dataType:'html',
          success:function(Result){
              $('#result').html(Result)
           }
       });
     });
   });

Controller Section

To retrieve form data within the controller function, use the following syntax:

$client = $this-input->post('client');

<div class="row">
    <form id="myForm" method="POST" action="">
        <div class="col-lg-6">
            <select id="clientSelect" name="customer" class="form-control">
                <option value="No Data">-- Select Customer --</option>
                <?php foreach ($customers as $customer): ?>
                    <option value="<?= $customer->id; ?>" id="<?= $customer->id; ?>" name="<?= $customer->name; ?>"><?= $customer->name; ?></option>
                <?php endforeach; ?>
            </select>
        </div>
        <div class="col-lg-6">
            <input type="button" class="submitBtn btn btn-success" id="submitButton" name="SubmitButton" Value="Submit"/>
        </div>
    </form>
</div>
<div id="resultSection"></div>
<script>
    $(document).ready(function(){
    $('#submitButton').click(function(event){
        event.preventDefault();
        $.ajax({
            url : "<?= base_url('Invoice/customerData') ?>",
            data: $('#myForm').serialize(),
            type : 'POST',
            dataType:'html',
            success:function(dataResult){
                $('#resultSection').html(dataResult)
            }
        })
    })
})
</script>

<!-- Controller -->
<?php
public function customerData() { 
    $customer = $this->input->post('customer'); 
    $this->view->load('Admin/customerView',$customer, TRUE); 
}

Modified form and controller to handle customer selection, please verify.

Data Retrieval Function

public function retrieveCities(){

  $this->db->order_by('city_id','desc');
  $this->db->limit('1000');
  $this->db->select('*,cities.name as city_name');
  $this->db->from('cities');
  $this->db->join('states','states.id=cities.state_id','left');
  $this->db->join('countries','countries.id=states.country_id','left');
  $data=$this->db->get();
  return $data->result_array();
}

private function getDatatablesQueryCity(){
    $column_search = array('cities.name','states.name','countries.country_name');
    $order = array('city_id' => 'desc');
    $column_order = array(null, 'city_name', 'sname', 'country_name', null);
    $this->db->select('cities.city_id,cities.name as city_name,states.name as sname,states.id as state_id,countries.id as country_id,countries.country_name');
     $this->db->from('cities');
     $this->db->join('states','states.id=cities.state_id','left');
     $this->db->join('countries','countries.id=states.country_id','left');
     $i = 0;
     foreach ($column_search as $item)
     {
        if($_POST['search']['value']) // if datatable send POST for search
            {
                if($i===0)
                {
                    $this->db->group_start();
                    $this->db->like($item, $_POST['search']['value']);
                }
                else
                {
                    $this->db->or_like($item, $_POST['search']['value']);
                }
                if(count($column_search) - 1 == $i)
                $this->db->group_end();
        }
        $i++;
    }
    if(isset($_POST['order']))
    {
        $this->db->order_by($column_order[$_POST['order']['0']['column']], $_POST['order']['0']['dir']);
    }
    else if(isset($order))
    {
        $order = $order;
        $this->db->order_by(key($order), $order[key($order)]);
    }
}
function retrieveDatatablesCity()
{
    $this->getDatatablesQueryCity();
    if($_POST['length'] != -1)
        $this->db->limit($_POST['length'], $_POST['start']);
    $query = $this->db->get();
    return $query->result();
}
function countFilteredCity()
{
    $this->getDatatablesQueryCity();
    $query = $this->db->get();
    return $query->num_rows();
}
public function countAllCity()
{
    $this->db->from('cities');
    return $this->db->count_all_results();
} 

Control Function

 public function displayCityList(){
        $this->load->view('admin/header');
        $this->load->view('admin/city');
        $this->load->view('admin/footer');
    }
    
    public function getCityAjaxData(){
        $list = $this->Admin_model->retrieveDatatablesCity();
        $data = array();
        $no = $_POST['start'];
        foreach ($list as $city){
            $no++;
            $row = array();
            $row[] = $no;
            $row[] = $city->city_name;
            $row[] = $city->sname;
            $row[] = $city->country_name;

            /* Additional HTML Markup */
            
            $data[] = $row;
        }
        $output = array(
            "draw" => $_POST['draw'],
            "recordsTotal" => $this->Admin_model->countAllCity(),
            "recordsFiltered" => $this->Admin_model->countFilteredCity(),
            "data" => $data,
        );
        echo json_encode($output);
    }

View Section

<div class="section-body">
    <div class="row">
        <div class="col-12">
            <div class="card">
                <div class="card-body">
                    <div class="table-responsive">
                        <table class="table table-striped" id="example">
                            <thead>
                                <tr>
                                    <th>Serial Number</th>
                                    <th>City Name</th>
                                    <th>State Name</th>
                                    <th>Country</th>
                                    <th>Management</th>
                                </tr>
                            </thead>
                        </table>
                    </div>
                </div>
            </div>
        </div>
    </div>
</div>
        
<!-- Modal for deletion confirmation -->
        
<div class="modal fade" id="delete" tabindex="-1" role="dialog" aria-labelledby="exampleModalCenterTitle" aria-hidden="true">
    ...
</div>

...