Like vaclav.blazek's answer, but instead of remove it, you can modify it.
Based on this documentation, you can change option that available in /etc/apt/apt.conf.d/20auto-upgrades.
// Do "apt-get update" automatically every n-days
// (0=disable, 1=1 day, 7= 1 week)
// Check new update.
APT::Periodic::Update-Package-Lists "0";
// Do "apt-get upgrade --download-only" every n-days
// (0=disable, 1=1 day, 7= 1 week)
// Download new update.
APT::Periodic::Download-Upgradeable-Packages "0"
// Do "apt-get autoclean" every n-days
// (0=disable, 1=1 day, 7= 1 week)
// Clean old updates.
APT::Periodic::AutocleanInterval "0";
// Run the "unattended-upgrade" security upgrade script
// every n-days
// (0=disable, 1=1 day, 7= 1 week)
// Requires the package "unattended-upgrades" and will write
// a log in /var/log/unattended-upgrades
APT::Periodic::Unattended-Upgrade "0";
So, if the scenario you want is to notify-only on daily update, it will looks like:
APT::Periodic::Update-Package-Lists "1";
APT::Periodic::Download-Upgradeable-Packages "0";
APT::Periodic::AutocleanInterval "0";
APT::Periodic::Unattended-Upgrade "0";
So, if the scenario you want is to download without upgrade on daily upgrade, it will looks like:
APT::Periodic::Update-Package-Lists "1";
APT::Periodic::Download-Upgradeable-Packages "1";
APT::Periodic::AutocleanInterval "0";
APT::Periodic::Unattended-Upgrade "0";
Or, if you want to do it all manually a.k.a disable it, it will looks like:
APT::Periodic::Update-Package-Lists "0";
APT::Periodic::Download-Upgradeable-Packages "0";
APT::Periodic::AutocleanInterval "0";
APT::Periodic::Unattended-Upgrade "0";
Basically, just zero it all.
There are two files that contain the configuration, namely:
/etc/apt/apt.conf.d/10periodic; and
/etc/apt/apt.conf.d/20auto-upgrades
So, check both files to make sure the configurations is as you need.
I hope this will you you.