In general, if you are using multiple e-mail clients (devices) for the same account, you are playing a dangerous game if you are using a pop3 connection for
any of your mail clients. That's why there is IMAP protocol.
Some servers (including Gmail, hence Kostya's questions), - do not offer for download e-mails ones downloaded via POP3 connection (unless a special configuration is used for setting up that connection).
Your best bet would be to change POP3 accounts to IMAP.
(Gmail has this workaround:
https://support.google.com/mail/answer/47948?hl=en , but I have no idea how Networksolutions POP3 and IMAP servers behave.)
PS.
Is your account configured as POP3 or IMAP (in AquaMail)?
it looks like POP3 on some IMAP on others
If you could be more specific in providing information, that would be more helpful.
Do you have more than one phone with Aquamail?
Originally, you wrote "when i view an email on Aquamail on my android it does not show up on my regular email client", which sounds as you have one phone and one "regular email client". If you could actually specify which one has POP3 and which one has IMAP, that would be more helpful.