Hello Mohamed jihad bayali,
Thank you for posting in Q&A forum.
Based on "but the AD schema version is in windows server 2003", I understand the AD schema you mentioned are Functional level (domain functional level and forest functional level).
And you can check it via PS command below:
(Get-ADForest).ForestMode
(Get-ADDomain).DomainMode

You mentioned "In fact, the customer, had these old domain controllers on win server 2003", so domain functional level and forest functional level should be 2003.
Ensure that all domain functional levels are equal to or higher than the forest functional level;
Ensure that all domain controller operating systems are at or above the domain functional level;
The domain function level can only be upgraded on the PDC simulation simulator operating host;
Forest functional levels can only be upgraded on schema operations host.
I want also to confirm when we say, starting from windows server 2012 schema update is done automatically, do we talk about the os version on the Domain controllers, or the OS version on the actual schema version?
A: I understand it is os version on the Domain controllers.
I hope the information above is helpful.
If you have any question or concern, please feel free to let us know.
Best Regards,
Daisy Zhou