Here I am explaining how to set or assign the value of ContextKey parameter for ASP.Net AJAX AutoCompleteExtender from Client Side using JavaScript
<%@ Register Assembly="AjaxControlToolkit" Namespace="AjaxControlToolkit" TagPrefix="cc1" %>
 
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
    <title></title>
    <script type="text/javascript">
        function SetContextKey() {
            $find('<%=AutoCompleteExtender1.ClientID>%').set_contextKey("221");
        }
    </script>
</head>
<body>
    <form id="form1" runat="server">
    <asp:TextBox ID="txtContactsSearch" runat="server" onkeyup="SetContextKey()"></asp:TextBox>
    <cc1:AutoCompleteExtender ServiceMethod="SearchCustomers" MinimumPrefixLength="2"
        CompletionInterval="100" EnableCaching="false" CompletionSetCount="10" TargetControlID="txtContactsSearch"
        UseContextKey="true" ID="AutoCompleteExtender1" runat="server" FirstRowSelected="false">
    </cc1:AutoCompleteExtender>
    </form>
</body>
</html>
 
 
Explanation:
Above I am setting the ContextKey property of the ASP.Net AJAX AutoCompleteExtender on the onkeyup event of the ASP.Net TextBox using the SetContextKey JavaScript function.
For more details on using the ContextKey Refer ASP.Net AJAX AutoCompleteExtender: Pass Additional Parameter to WebMethod using ContextKey