There is no mini.iso for Ubuntu 20.10. Not the same, but you can install minimal system using debootstrap.
To show this method, I will use Ubuntu 20.10 live iso booted from usb. In terminal:
sudo su -
# Install debootstrap
apt update
apt install debootstrap
Partitioning
fdisk -l
mkfs.ext4 /dev/sdaX
mount /dev/sdaX /mnt
Install base packages
debootstrap groovy /mnt
mount /dev /mnt/dev --bind
mount /proc /mnt/proc --bind
mount /sys /mnt/sys --bind
Go inside new system
chroot /mnt
Install the Linux kernel and text editor
apt update
apt install linux-image-generic nano
Check UUID and paste it into /etc/fstab
blkid | grep sdX > /etc/fstab
Edit fstab so it looks like this:
UUID=<your uuid> / ext4 errors=remount-ro 0 1
nano /etc/fstab
Install boot-loader (Legacy BIOS)
On UEFI, change the target to i386-efi
grub-install --target i386-pc /dev/sdX
Optionally, edit grub settings in /etc/default/grub
update-grub
Add user
adduser <name>
usermod -aG sudo <name>
passwd <name>
Set time and language
dpkg-reconfigure locales
dpkg-reconfigure tzdata
dpkg-reconfigure keyboard-configuration
Set hostname
nano /etc/hostname
Fix NetworkManager if you install this way:
Ethernet device not managed