Hi nauna,
Check this example. Now please take its reference and correct your code.
HTML
<script type="text/javascript" src="https://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
<script type="text/javascript">
$(function () {
$("[id*=CheckBoxList1]").bind("click", function () {
$("[id*=CheckBoxList2]").hide();
if ($("[id*=CheckBoxList1] input:checked").length > 0) {
$.each($("[id*=CheckBoxList1] input:checked"), function () {
if ($(this).val() == 'Two') {
$("[id*=CheckBoxList2]").show();
}
});
}
});
});
</script>
<asp:CheckBoxList ID="CheckBoxList1" runat="server">
<asp:ListItem Text="One" Value="One" />
<asp:ListItem Text="Two" Value="Two" />
</asp:CheckBoxList>
<br />
<asp:CheckBoxList ID="CheckBoxList2" runat="server" Style="display: none">
<asp:ListItem Text="Mango" Value="Mango" />
<asp:ListItem Text="Apple" Value="Apple" />
</asp:CheckBoxList>
Screenshot
