I keep receiving notifications about the deadline to file my taxes but I already filed last month and received my refund. How do I let TurboTax know I paid my taxes?

If you have more than one TurboTax account, the other one is likely generating the "reminder" emails.  If you know that you filed, the return was accepted, and your return has been processed, then ignore those emails.

And...TurboTax never knows if you paid your tax due.  The IRS does not tell TT If you paid.  Your account will always show that you had tax due---which was the result of the return you prepared using the software.