Grab the kernels and intramfs from this pack
It has a guaranteed to work (on Pro) 4.14 kernel and 4.20 and 5.3 kernel (with hdmi unplug trick)
For now I recommend 4.14 file.
Rename that file only to BzImage.
Choose a distro for yourself. Since you ddn't tell me which model PS4 you have I'm going to assume you havea base machine by sales numbers. (lol)
For base machine grab ITmania's Fedora 32 updated from here:
https://drive.google.com/file/d/1TXxnoHHzexPRY4ECvpghhewIwYpzwQ4D/view
Use an external USB Hard drive and format it as MBR and Fat32 as single partition.
You can use a free tool like minitool partition manager for this.
After you download ITmania's fedora rename it as psxitarch.tar.xz
Copy the 4.14 kernel (BZImage) the intramfs and psxitarch.tar.xz files into the USB drive.
Plug it in the console.
From console internet browser if you are on 6.72, go to sleirsgoevy's host
https://sleirsgoevy.github.io/ps4jb
If you are on other firmwares, try darkmodder's one:
https://darkmoddervc.github.io/ps4jb/
Enable jailbreak then enable the linux payload.
When the shell comes up type
exec install-psxitarch.sh
This will start installing Fedora 32.
After the installation is done, you can start using it.
The user password is ITmania
As for graphics drivers, ITmania's repo has older rpm drivers for Fedora. f you havegraphics problems, type this in terminal:
cd /etc/yum.repos.d/
sudo wget
https://raw.githubusercontent.com/IT-mania/RPMS-ST/master/ps4_.repo
sudo dnf update --refresh --repo ps4_
sudo dnf install mesa-dri-drivers-20.3.4-2.fc32.i686 mesa-libEGL-20.3.4-2.fc32.i686 mesa-libGL-20.3.4-2.fc32.i686 mesa-libd3d-20.3.4-2.fc32.i686 mesa-libgbm-20.3.4-2.fc32.i686 mesa-vulkan-drivers-20.3.4-2.fc32.i686 --repo ps4_