How to retrieve only new emails using POP3 protocol

POP3 does not have the capibility to track whether messages are read or unread. I would suggest you set your limit to a finite number such as 50 or 100. Perhaps you could do some sort of pagination system.

This code needs to be within a function so that you can call it like so:

Sub Main
    Dim start As Integer = Integer.parse(Request.QueryString("start"))
    Dim count As Integer = Integer.parse(Request.QueryString("count"))
    Dim subjects As New List(Of String)
    subjects = getSubjects(start, count)

    'Do whatever with the results...
    '
End Sub

Function getSubjects(ByVal startItem As Integer, ByVal endItem as Integer) As List(Of String)
   Dim popp As New Pop3Client("user@mail.com", "*******", "pop3.mail.com")
    popp.AuthenticateMode = Pop3AuthenticateMode.Pop
    popp.Port = 110

    popp.Authenticate()
    Dim msglist As New List(Of String)

    If popp.State = Pop3ConnectionState.Authenticated Then
        Dim totalmsgs As Integer = popp.GetTotalMessageCount()
        Dim endItem As Integer = countItems + startItem
        If endItem > totalmsgs Then
            endItem = totalmsgs
        End If

        If totalmsgs > 0 Then
            For index As Integer = startItem To endItem
                Dim msg As Pop3Message = popp.GetMessage(index)
                msglist.Add(msg.Subject)

            Next

            popp.Close()
        End If
    End If
    Return msglist
End Function

Just have the program change the value for startItem to 50 get the next fifty (items 50-100)

I found out that OpenPop.Pop3.AuthenticationMethod.UsernameAndPassword is the missing part. I have modified the code to be following and it works.

OpenPop.Pop3.Pop3Client PopClient = new OpenPop.Pop3.Pop3Client();
PopClient.Connect("pop.secureserver.net", 995, true);
PopClient.Authenticate("username", "pass", OpenPop.Pop3.AuthenticationMethod.UsernameAndPassword);