Hi there, Icythrillz.
After reviewing your post, it appears when you receive a notification while you're using the Music application, the music playback stops. I'm happy to help.
When the music stops, does it resume again as normal after the notification sound comes in? If so, this would be expected behavior. If not, please follow these steps to troubleshoot the issue:
How to force an app to close on your iPhone, iPad, or iPod touch -- First, force close the Music application if it's open, then -- Restart your iPhone, iPad, or iPod touch -- Once it's returned to the Home screen, test the issue.
How to check the storage on your iPhone, iPad, and iPod touch -- If restarting your iPhone didn't resolve the issue, you can offload the Music application, then reinstall it again. Go to Settings > General > iPhone Storage, scroll to the Music application and tap "Offload App". Once the application has been removed, reinstall it again and test.
Let me know how that goes.
Take care!