First thing to try.
Quit the Mail.app first and using the Finder, go to Home > Library > Mail > this POP account named folder (named by the user name and incoming mail server for the account) > MessageUidsAlreadyDownloaded2.
Delete the MessageUidsAlreadyDownloaded2 file and empty the Trash.
Launch Mail and if successful, any previously downloaded messages that remain on the server will be downloaded again along with any new messages on the server not yet downloaded. A new MessageUidsAlreadyDownloaded2 file will be created automatically by Mail within the account named folder.
If this isn't successful, locate the first message available on the server not yet downloaded by Mail. Assuming you have webmail access for this account, view this message via webmail. If you don't need to save it, delete it from the server via webmail access or via the Mail.app "Mail on Server" option. If you need to save this message and your are able to create folders on the server via webmail access to save messages, do so and transfer this message to the created folder or mailbox and then check if this resolves the problem with Mail downloading the remaining messages available on the server.