After looking into your scenario i have prepared one sample for this scenario for you.
I have a asp server textbox control in my page like as below :-
<asp:textbox id="txtTest" text="" runat="server" autopostback="true" ontextchanged="txtTest_TextChanged" clientidmode="Static"></asp:textbox>
The TextChanged event handler code is as follows in cs code behind for example :-
protected void txtTest_TextChanged(object sender, EventArgs e)
{
Response.Write("Success Test");
}
Now in jQuery on document ready handle the keyup event as below to fire the server side TextChanged event on more than 6 character as below :-
$(function () {
$("#txtTest").keyup(function (e) {
if ($("#txtTest").val().length > 6) {
__doPostBack('<%# txtTest.ClientID %>', 'OnTextChanged')
}
});
});
Hope this will also be working for you.
Please let me know if any kind of problem you are facing with this code example to get your issue resolve.