How do I clear spam e-mails to fake addresses on my domain?

Part of the issue here is that you are simply allowing any email to your domain to work vs letting them :fail:

in cPanel NEVER SET A DEFAULT ADDRESS TO FORWARD ALL MAIL - but rather set it as

:fail: no Such User Here Now Go Away and Spam someone else

Why you should use :fail:

There are sound technical reasons that you should only use :fail: and not :blackhole: on a cPanel server running exim.

In general the two different settings both discard email not destined for a POP3 account, an alias or a catchall alias. However, ever since cPanel included the verify = recipient code in the standard cPanel ACL section for exim, the way email is discarded differs with the two methods quite starkly:

Using :blackhole:

email is accepted and received into the server in its entirety. It is then processed through exim and only on delivery is it written to the null device (/dev/null) and silently ignored. This wastes server bandwidth as the email data, or body, of the email is accepted into the server.
This wastes server resources (CPU, memory and disk I/O) as the email is fully processed by exim before being finally written to /dev/null Because the blackholed email is still processed through the whole of exim before it is finally deleted, if any of the usual checks and routing that any email goes through fails, such email can be placed in the exim mail queue for later reprocessing. This can lead to tens of thousands of blackholed emails accumulating in the exim mail queue which in turn can cause a range of serious server performance and resource problems and will affect the normal and timely delivery of email

This actually breaks the SMTP RFC's because you're not notifying the sending SMTP server that the email is undelivered, which is a requirement Causes emails that will never be delivered onto the exim mail queue because checks such as sender verification are still carried out when processing such emails and if they cannot complete they will stay on the exim mail queue and repeatedly reprocess the email until it is finally discarded (usually 4+ days). This can cause very large mail queues full of spam which is repeatedly processed causing severe performance degradation

Using :fail: the email is never accepted into the server. During the initial SMTP negotiation when the senders SMTP server connects to your SMTP server, the sending SMTP server issues a RCPT command notifying your server which email address the email to follow is intended for. Your server then checks whether the recipient email actually exists on your server (a POP3 account, an alias or a catchall alias) and if it does not, it issues an SMTP DENY which terminates the attempt to deliver the email.

• This saves bandwidth as the email data is never received into your server
• This saves server resources as the email never has to be processed
• This complies with the SMTP RFC's because the sending SMTP server receives the DENY command
• Your server does not send a bounce message (just the DENY command)
• Your server does not send anything to the sender of the email (i.e. the address in the From: line)
• The sending SMTP server is responsible for notifying the original sender

Here is a simple explanation of what happens during the SMTP conversation

1. Some other SMTP server connects to your server on port 25 and initiates an SMTP connection (EHLO command)
2. Other server then sends a message saying who they're delivering a message for (MAIL FROM command)
3. Other server then sends who the message is for on your server (RCPT command)
4. At this point your server then checks whether the email address in the RCPT command can actually be delivered on your server. If you do not have a catchall alias configured to point to an email address (Default Address) and you have it set to :fail: the following happens:
5. Your server sends back along the same connection to the sending server "Go away, no-one here" (the DENY command)
6. The sender server would then normally tell their user that the attempt to email your server failed. Your server does not send a "bounce" message.

Using :fail: is wise - because As far as your server is concerned, all that has happened is a little SMTP chatter and no email has been received and no bounce sent

special thanks to Chirpy on the cpanel forums for an excellent write up and his work with configserver to help with this post.

This appears to be a backscatter attack.
More about rejecting these emails here:
http://spamlinks.net/prevent-secure-backscatter.htm