I created a CustomExceptionClass that its messages are from a configuration file and are a friendlier message to the user.
Then I want to log wich exception was thrown because, if something went wrong, I want to know details then I can fix this. So, I have a doubt.
Where to log these exceptions using log4j? Inside the CustomExceptionClass, or I let the method that throws this exception log it?
You should log wherever you are catching the Exception. If you are not catching it anywhere it really depends how you are running your application.