Hello klaradumas.
Thank you for using Apple Support Communities. It sounds like you're experiencing issues with your notification sounds. Specifically, notification sounds come in very low while listening to music on speaker mode. We can understand how this would be an issue. Allow us to investigate this issue and assist in any way we can.
For help with sound/audio issues, you'll want to review the helpful resources below:
Adjust audio and visual settings on iPhone - Apple Support
If you hear no sound or distorted sound from your iPhone, iPad, or iPod touch speaker - Apple Support
You'll find great recommended troubleshooting steps you can try. Additionally, if you have any pending updates available for your iPhone, please create a backup and update your device. Keeping it fully updated can help resolve various issues and also help with over all performance. Just in case, the resources below can help:
How to back up your iPhone, iPad, and iPod touch - Apple Support
Update your iPhone, iPad, or iPod touch - Apple Support
We hope this information is useful. Feel free to keep us updated. Cheers.