I waited for my favorite time zone of in the morning.
Does the sentence above make sense? I mean that time zone is 'the range of time' in this sentence.
You mean to say time of day or time of the day.
The evening is my favorite time of (the) day.
Early morning is my favorite time of (the) day.
No, a time zone is a place in the world where people set their clocks in a particular way, e.g. China Time Zone, Eastern Time Zone or Europe/London.