Veeam Agent for Linux 4.0 is the last veeam agent which supports Debian 8.

https://helpcenter.veeam.com/archive/agentforlinux/40/userguide/system_requirements.html

For vm backups which uses application aware processing, Veeam Backup & Recovery V10 was the last version with support for Debian 8:

https://helpcenter.veeam.com/archive/backup/100/vsphere/platform_support.html

VMs with crash consistent backups are supported in all Veeam Backup & Replication versions as long the hypervisor supports Debian 8 as a vm guest operating system.

Thanks

Fabian

If I use Debian 10, can I do backups smoothly? And if I want to use version 11, which is now stable, does Veeam back up?

Debian 10 + 11 are both supported and tested with the latest veeam versions:

Veeam Backup & Replication v11a:

https://helpcenter.veeam.com/docs/backup/vsphere/platform_support.html?ver=110

Veeam Agent for Linux 5.0:

https://helpcenter.veeam.com/docs/agentforlinux/userguide/system_requirements.html?ver=50

​Perfect collocation of @Mildur . If you install the latest version of Veeam Agent Linux (5.0), it supports until Debian 9. 
Probably you need install an older version of Veeam Agent Linux like the 4.0.
​

Okay, thanks a lot guys for the support. A great week for us!!