Correct way for Codeigniter AJAX get data from MySQL database without refreshing

you can use result_array(); if you are retrieving more than one row. it will return pure array.

function cashbook_items()
{
    $this -> db -> select('name');
    $this -> db -> from('items');
    $query = $this -> db ->get();

    return $query -> result_array();
}

then in your view:

$('#btnList').click(function(e){
    $.ajax({
        url:"<?php echo base_url();?>/cashbook/get_item",
        dataType:'text',
        type:"POST",
        success: function(result){
            var obj = $.parseJSON(result);
            console.log(obj);
           // $.each(result.results,function(item){
           //     $('ul').append('<li>' + item + '</li>')
           // })
        }
    })
    $('#div_list').toggle(900)
})

you can check what the obj returns using console.log(obj);

$.parseJSON(result); will result in the conversion of the encoded json to an array of object.

if you want to access the Parsed JSON, use the ff.

obj[0]

this indicates that you will return the first row of your query.

obj[0]['name'];

to access individual columns, you can use the name of that column. which you stated in your model.

$('#btnList').click(function(e){
    $.ajax({
        url:"<?php echo base_url();?>/cashbook/get_item",
        dataType:'text',
        type:"POST",
        success: function(result){
            var obj = $.parseJSON(result);
            $.each(obj,function(index,object){
                $('ul').append('<li>' +object['name']+ '</li>');
            })
        }
    })
    $('#div_list').toggle(900)
})

Edit:

In you View.

  <style>
    ul {
        list-style-type: none;
    }
</style>
<div align="center" style="padding-top: 1%" id="div_main">
    <div class="jumbotron">
        <h1>Cashbook Items</h1>

        <p>Add items to to cashbook so they used <br>when adding incomings and out goings later</p>

        <form id="items_form" data-abide>
            <div class="large-3 large-centered columns">
                <label>New Item Name
                    <input type="text" required name="item" id="item_name">
                </label>
                <small class="error">No item added</small>
            </div>

            <button class="button radius" id="btnItem">Submit</button>
        </form>
        <a href="#" data-reveal-id="firstModal" class="radius button" id="btnList">Item List</a>
    </div>

</div>

<div class="row">
    <div id="firstModal" class="reveal-modal" data-reveal align="center">
        <h3>Current Items</h3>

        <p>Reccuring Items in the database</p>
        <ul id="list_item">
        </ul>
    </div>
</div>
</div>
<br>
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1/jquery.min.js" type="text/javascript"></script> 
<!--dont forget to add your jquery if you are using jquery functions and methods! -->
<script>
$(document).ready(function(){ //remember to put document.ready function when you are using jquery then insert your jquery functions inside.
    $('#btnList').on('click',function (){
        $.ajax({
            url: "<?php echo base_url();?>index.php/cashbook/get_item",
            dataType: 'text',
            type: "POST",
            success: function (result) {
                var obj = $.parseJSON(result);
                $.each(obj,function(index, object) {
                    $('#list_item').append('<li>' + object['name'] + '</li>');
                });
            }
        })
    });


    $('#items_form').submit(function (e) {
        e.preventDefault();
        var yourItem = $('#item_name').val();
        $.ajax({
            url: "<?php echo base_url();?>/cashbook/new_item",
            type: 'POST',
            data: {data:yourItem},
            success: function (data) {
                alert('THIS WORKED');

            },
            error: function () {
                alert('Nah died');
            }

        })
    });

});
</script>

Your Controller:

<?php if ( ! defined('BASEPATH')) exit('No direct script access allowed');

class cashbook extends CI_Controller{
    function __construct() {
        parent::__construct();
            $this->load->helper('url');
            $this->load->database();
            $this->load->model('M_cashbook');
    }

    function index(){
        $this->load->view('load_your_view_here'); //load your view here if you are using index as your default action when loading the default controller.
    }

    function items(){
        $data['items'] = $this ->get_item();
        $this->load->view('/holders/header');
        $this->load->view('/cash/v_cashbook_items_page',$data);
        $this->load->view('/holders/footer');
    }

    function get_item(){
        $data = $this->input->post('data');
        $data = $this -> M_cashbook -> cashbook_items();
        echo json_encode($data);
    }
}