What is the name of the core fortified area of a town or city?

the keep was the final place of Defense

Hear this in the bible often enough! so I know what one finally looks like! and what a citadel is! but I got it right!

A keep is the final defensive core of a castle, not of a town or city. Though it may be true that some citadels were designed with the equivalent of a keep in them.

I agree 👍. The keep is the correct answer.