How can we find which user is authenticating from which DC.

you can use
set L
command on the workstation to get the logonservers.

create a script around it

This is actually difficult - getting the last logon time is fairly easy but the authenticating server is not so easy(!).

Not sure it's going to be attainable by script.

However, there might be tools that can do it for free:

http://www.manageengine.com/products/free-windows-active-directory-tools/free-windows-active-directory-query-tool.html

http://maxpowersoft.com/adreportslite.php

VBScript to report user name & logon time (use cscript otherwise, you get a popup for every username in wscript - save it to a file, then cscript file.vbs from a command prompt):

intBias = TimeZoneBias
arrAttributes = Array("lastLogonTimeStamp","displayname","mail")
 
Set adoCommand = CreateObject("ADODB.Command")
Set adoConnection = CreateObject("ADODB.Connection")
adoConnection.Provider = "ADsDSOObject"
adoConnection.Open "Active Directory Provider"
adoCommand.ActiveConnection = adoConnection
 
Set objRootDSE = GetObject("LDAP://RootDSE")
strBase = "<LDAP://" & objRootDSE.Get("defaultNamingContext") & ">"
Set objRootDSE = Nothing
 
strFilter = "(&(objectCategory=person)(objectClass=user))"
strAttributes = Join(arrAttributes,",")
Wscript.Echo Join(arrAttributes,";")
strQuery = strBase & ";" & strFilter & ";" & strAttributes & ";subtree"
adoCommand.CommandText = strQuery
adoCommand.Properties("Page Size") = 100
adoCommand.Properties("Timeout") = 30
adoCommand.Properties("Cache Results") = False
Set adoRecordset = adoCommand.Execute
Do Until adoRecordset.EOF
    On Error Resume Next
    strTempOutput = ""
    For i = 1 To Ubound(arrAttributes)
        strTempOutput =  strTempOutput & " ; " & adoRecordset.Fields(arrAttributes(i)).Value
        strOutput = Mid(Ltrim(strTempOutput),3)
    Next
    Set objDate = adoRecordset.Fields(arrAttributes(0)).Value
    If (Err.Number <> 0) Then
        dtmDate = #1/1/1601#
    Else
        dtmDate = ((((objDate.Highpart * (2^32)) + objDate.LowPart)/(600000000 - intBias))/1440) + #1/1/1601#
    End If
    Set objDate = Nothing
    Wscript.Echo strOutput & " ; " & dtmDate
    adoRecordset.MoveNext
Loop
adoRecordset.Close
adoConnection.Close
Set adoRecordset = Nothing
Set adoConnection = Nothing
Set adoCommand = Nothing
 
Function TimeZoneBias
    strComputer = "."
    Set objWMIService = GetObject("winmgmts:{impersonationLevel=impersonate}!\\" & strComputer & "\root\cimv2")
    Set colTimeZone = objWMIService.ExecQuery("Select * from Win32_TimeZone")
    For Each objTimeZone in colTimeZone
        TimeZoneBias = objTimeZone.Bias
    Next
    Set colTimeZone = Nothing
    Set objWMIService = Nothing
End Function