Can we say "Duo özellikle" in this sentence instead of "özellikle Duo"?
Yes, you can. Though it might not be accepted since we don't include every possible word order. But it's possible to say that.
AlexinNotTurkey told me that modifiers always come before the things they modify, so why don't I see "çok iyi" as a modifier for "öğrencilerim"?? “Benim çok iyi öğrencilerim, özellikle Duo.”
Because that would mean "my very good students" :) This isn't a modifier, but rather a predicate.
A great way to figure out if it is a modify vs. a predicate is to see if ti can answer the question "which X"
I believe it ;-)
Can we use esas (or sth like that) instead of özelikle?
It is not commen saying in a sentence like this
Why is "Benim öğrenciler çok iyi, özellikle Duo" not right?
Benim öğrenciler is colloquial streettalk. The correct form is benim öğrencilerim.