Hello
As far as I know, the old Apple TV box has a mini-jack optical connection.
Do I understand correctly that you want to connect the Apple TV to a device/amplifier with a coaxial connection?
This is not possible without a converter, because one is an optical signal and the other is an electrical signal...
There are no cables that can do this (logical or not).
Most converters are TOS-COAX, for the connection to the box you need a TOS-to-Mini-Jack cable.
For the connection to the device/amplifier you then need a simple digital COAX cable.

Thank you very much, now I understand.