I want to make a portable version of Linux Ubuntu
Solution 1:
Full Install vs Persistent install
Consider doing a Full install to USB, It does not suffer from the irritating 20.04 disk check problem when booting.
A Full install USB and a Persistent install USB both save data and installed programs after reboot.
Comparison between Persistent and Full install USB
Advantages of a persistent install:
1) You can use the persistent pendrive to install Ubuntu to another computer.
2) A persistent install takes up less space on the pendrive.
3) You can reset the pendrive by overwriting the old casper-rw file with a new one.
4) The install to pendrive takes less time.
Advantages of a Full install:
1) You can update and upgrade.
2) If you have problems or wish to modify, the solution is the same as with an internal install, (You can ask for help in these forums).
3) No ugly startup / install screen.
4) Better security, you can use full encryption
5) You can use proprietary drivers.
6) Hibernation works.
7) A persistent install is limited to a 4GB casper-rw and a 4GB home-rw persistence file, to get more persistence requires persistence partitions. Once casper-rw is full, the drive will not boot.
8) More efficient usage of disk space. Does not require reserved space for persistence.
9) Faster boot, no automatic disk checking or Try Ubuntu/Install Ubuntu screen.
10) You can run VBox and use virtual machines.
Note that once booted, both methods run at about the same speed.
Full Install Method
One method for creating a Full install USB: How to Create a Full Install of Ubuntu 20.04 to USB Device Step by Step