voicemail badge won't go away when I don't have voicemail service on the carrier

 Try and Force Restart your iPhone EXACTLY as shown below and see whether that resolves the issue:

• Press and quickly release Volume UP button
• Press and quickly release Volume DOWN button
• Press and Hold the SIDE button until an Apple logo appears and then release the Side button (Can take up to 20 seconds. (DO NOT release Side Button when invited to Slide Power OFF). 

Axel F.

Can you contact your carrier and have them reset the Voicemail for your account and see whether that resolves the issue?

Axel F.

It would be better if you can please re-post with a screenshot, in order to understand the phenomenon better. Images/pictures speak louder than words. 

Please understand this is a public forum: While attaching a Screenshot, do not provide any personal credentials, such as IP address, Card detail, email id, apple id, IMEI number, Serial Number, Phone number, Order ID, if you are sharing a map ensure your location is not identifiable, etc.

With the limited information that you have provided, It is hard to even guess the problems faced by you. 

You may get faster and better responses to your query by --> Writing an effective Apple Support Commun… - Apple ...

Please re-post with detail so that someone else can help.