System.notsupportedexception: the requested security protocol is not supported

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Windows

TLS

I have developed one application in .net 3.5 framework and consuming web service through it using below code

In our development application it's running fine but when I have deployed it in production environment It's giving me an error. I have tested it in three different OS Windows 7, Windows Server 2008 R2 and Windows Server 2003 R2

System.NotSupportedException: The requested security protocol is not supported.

Do I need to install any additional software or patch?

I have gone through Microsoft Support[^]

But when I install this patch I am getting error "This patch is not applicable to your system"

What I have tried:

Module SslProtocolsExtensions
    Public Const Tls12 As SslProtocols = CType(&HC00, SslProtocols)
    Public Const Tls11 As SslProtocols = CType(&H300, SslProtocols)
End Module

Module SecurityProtocolTypeExtensions
    Public Const Tls12 As SecurityProtocolType = CType(SslProtocolsExtensions.Tls12, SecurityProtocolType)
    Public Const Tls11 As SecurityProtocolType = CType(SslProtocolsExtensions.Tls11, SecurityProtocolType)
    Public Const SystemDefault As SecurityProtocolType = CType(0, SecurityProtocolType)
End Module

Dim response As String
        Dim client As New WebClient()
        Dim credentials As String

        credentials = Convert.ToBase64String(Encoding.ASCII.GetBytes("XXXX" + ":" + "XXXX"))
        client.Headers.Add("Authorization", "Basic " & credentials)
        client.Headers.Add(HttpRequestHeader.ContentType, "application/xml")
        If blnCookie Then
            client.Headers.Add(HttpRequestHeader.Cookie, strCookie)
        End If

        ServicePointManager.SecurityProtocol = SecurityProtocolType.Tls Or SecurityProtocolType.Ssl3 Or SecurityProtocolTypeExtensions.Tls11
        Try
            Dim strEaushadhiURI = "https://XXXXXXXXXXX/AMH/1031180700004"
            System.Net.ServicePointManager.ServerCertificateValidationCallback = _
  Function(se As Object, _
  cert As System.Security.Cryptography.X509Certificates.X509Certificate, _
  chain As System.Security.Cryptography.X509Certificates.X509Chain, _
  sslerror As System.Net.Security.SslPolicyErrors) True
            response = client.DownloadString(New Uri(strEaushadhiURI))
            System.Net.ServicePointManager.ServerCertificateValidationCallback = Nothing
            TextBox1.Text = response
        Catch ex As WebException
            Throw ex
        End Try