We use mail.dll to get mails via Pop3. Is it possible to check new mails first and download them and afterwards check already received mails?
POP3 protocol doesn't have a concept of seen and unseen massages.
Most POP3 servers however assign unique, persistent id (uid) to each email message (you can learn more on this in Unique ID in POP3 protocol article).
So what you can do, is to use Pop3.GetAll method to retrieve all uids first. Then filter this list, using uids stored on previous run. This way you will have a list of new uids.
This sample may also help you: https://www.limilabs.com/blog/receive-unseen-emails-using-pop3