Here I have created sample that full-fill your requirement.in this on button click you will get selected child check box in Javascript as well as in code behind.
HTML
<div>
    <asp:TreeView ID="TreeView1" runat="server" ShowCheckBoxes="All">
    </asp:TreeView>
    <script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
    <script type="text/javascript">
        $(function () {
            $("[id*=TreeView1] input[type=checkbox]").bind("click", function () {
                var table = $(this).closest("table");
                if (table.next().length > 0 && table.next()[0].tagName == "DIV") {
                    //Is Parent CheckBox
                    var childDiv = table.next();
                    var isChecked = $(this).is(":checked");
                    $("input[type=checkbox]", childDiv).each(function () {
                        if (isChecked) {
                            $(this).attr("checked", "checked");
                        } else {
                            $(this).removeAttr("checked");
                        }
                    });
                } else {
                    //Is Child CheckBox
                    var parentDIV = $(this).closest("DIV");
                    if ($("input[type=checkbox]", parentDIV).length == $("input[type=checkbox]:checked", parentDIV).length) {
                        $("input[type=checkbox]", parentDIV.prev()).attr("checked", "checked");
                    } else {
                        $("input[type=checkbox]", parentDIV.prev()).removeAttr("checked");
                    }
                }
            });
        })
        function GetSelected() {
            var childCheckBox = '';
            var parentCheckBox = '';
            var chkparent = $('[alt*=Collapse]').closest('tr').find('input[type=checkbox]').next('a').each(function () {
                parentCheckBox = parentCheckBox + $(this)[0].innerText + ',';
            });
            var chkChilds = $("input[type=checkbox]:checked").each(function () {
                childCheckBox = childCheckBox + $(this).next('a')[0].innerText + ',';
            });
            var chkChilds = childCheckBox.substring(0, (childCheckBox.lastIndexOf(','))).split(',');
            var chkparent = parentCheckBox.substring(0, (parentCheckBox.lastIndexOf(','))).split(',');
            var result = $.grep(chkChilds, function (el) {
                return $.inArray(el, chkparent) == -1;
            });
            var resultStr = result.join(',');
            $('[id*=hfSelected]').val(resultStr);
            alert('Selected Child : ' + resultStr);
        }
    </script>
    <asp:Button Text="Get Selected" runat="server" OnClientClick="GetSelected()" OnClick="GetSelected" />
    <input id="hfSelected" type="hidden" runat="server" />
</div>
Code
protected void Page_Load(object sender, EventArgs e)
{
    if (!IsPostBack)
    {
        TreeNode treeNode = new TreeNode("Fruits", "Fruits");
        treeNode.ShowCheckBox = true;
        TreeView1.Nodes.Add(new TreeNode("Fruits", "Fruits"));
        TreeView1.Nodes[0].ChildNodes.Add(new TreeNode("Mango", "Mango"));
        TreeView1.Nodes[0].ChildNodes.Add(new TreeNode("Apple", "Apple"));
        TreeView1.Nodes[0].ChildNodes.Add(new TreeNode("Pineapple", "Pineapple"));
        TreeView1.Nodes[0].ChildNodes.Add(new TreeNode("Orange", "Orange"));
        TreeView1.Nodes[0].ChildNodes.Add(new TreeNode("Grapes", "Grapes"));
        TreeView1.Nodes.Add(new TreeNode("Vegetables", "Vegetables"));
        TreeView1.Nodes[1].ChildNodes.Add(new TreeNode("Carrot", "Carrot"));
        TreeView1.Nodes[1].ChildNodes.Add(new TreeNode("Cauliflower", "Cauliflower"));
        TreeView1.Nodes[1].ChildNodes.Add(new TreeNode("Potato", "Potato"));
        TreeView1.Nodes[1].ChildNodes.Add(new TreeNode("Tomato", "Tomato"));
        TreeView1.Nodes[1].ChildNodes.Add(new TreeNode("Onion", "Onion"));
    }
}
protected void GetSelected(object sender, EventArgs e)
{
    string seleted = hfSelected.Value;
}
Screenshot
