voicemails are delvered 2-3 weeks later

Hi, sosojun!

Thanks for visiting the Apple Support Communities. If I understand your issue, you are not receiving voicemails in a timely manner, up to 3 weeks after they're originally left. I'm happy to help!

With voicemail being a carrier-provided and supported feature, it's good to see you've already spoken with AT&T. To make sure the issue does not lie with your iPhone, we can use the following troubleshooting from Set up Visual Voicemail on your iPhone - Apple Support:

"Get help with Visual Voicemail

If you can't set up Visual Voicemail, contact your carrier to make sure that your plan supports the feature. 

If you need help, try these steps. Check your Visual Voicemail after each step:

1. Make sure that you have the latest version of iOS.
2. Check for a carrier-bundle update: Go to Settings > General > About. If an update is available, a message will ask you to update.
3. To check your cellular network connection, try to call someone. 
4. Make sure that you set up your voicemail. To check, dial your own phone number from your iPhone and leave yourself a message.
5. Call your iPhone from another phone and try to leave yourself a voicemail.
6. Go to the keypad and press and hold on the 1, or press the Call Voicemail button. This dials voicemail. Check if you have any missed messages.
7. On the Voicemail screen, tap Greeting. Then change your greeting to either custom or default. 
8. If you have more than one cellular plan on your iPhone, try switching to the other plan. Call the first number and try to leave a message.
9. Go to Settings > General > Reset and tap Reset Network Settings.
10. If you still need help, contact your carrier."

Best!