Hi ,
I am having intel server board which is having issue with onboard USB ports (not working /not repairable) and only way to connect mouse/keyboard using USB . For time being I am using pci to usb adapter , so after booting OS I can use I/O devices .

Is there any way to install Centos/ubuntu on that .

Probably yes, since the installation kernel is very likely to support PCI, USB and this combination.

You can try this without installing anything. Go through the first screens before anything is written to storage,

Wait ... Why install LTS distroes instead of rolling ones on servers? Inside rollings HardenedBSD-CURRENT is best, Artix and Alpine are secondary better ones.

Only thing is how to boot OS on this scenario . DVD-ROM ,Network option is there but keyboard/mount won't work to navigate .
Is there any script to automate OS install ?

you need to boot ubuntu from pendrive (for example). Most probably if you could boot an OS it will be able to handle your keyboard/mouse and complete the install onto your HDD.
If you cannot access BIOS, because it cannot handle that keyboard you will be stuck. Servers may have access using serial console, that can be another way to configure boot order or select boot device.

Other then a real server (see below) the board needs to be able to automatically boot from some device i.e. CD/DVD, USB, PXE or possibly the hard drive.

With CentOS and Ubuntu (it used to) you can use a kickstart file to automatically install the operating system. You can remaster the ISO file to add the kickstart file location if needed.

https://docs.centos.org/en-US/centos...de/Kickstart2/

As stated some servers like HP and Dell have a special option (IPMI or DRAC) where you can access the BIOS from a network device.

It is also possible to boot the ISO using grub2 from a hard drive. I have never tried from scratch but it should be possible to install it from another PC.