This riddle strongly reminds me of:
TARDIS(Time and Relative Dimension In Space) from the series "Doctor Who"
I have a long history from east to west,
to some I'm the worst and others the best.
The name says it all! It has a long history (It's a time machine!) and it has that history from east to west (It's also a transport device. It also travels through dimensions!). Its good for the universe and bad especially for the DALEKS.
With a core made of resin I dance and I flutter,
no one judges me when I speak with a stutter.
I do not remember about the TARDIS core but the dance and flutter reference may be to how it operates in the show. No one judges the TARDIS!
I may be an object of legend or myth,
at first you won't find me but maybe in fifth.
The TARDIS and Doctor Who is a kind of legendary series and both of them are known as legends or myth in the series as well. Not sure about the first and fifth reference.
For at any point, you summon power of three,
And look to the wind, you may just find me.
Power of three is an episode of Doctor Who and one can find TARDIS in the wind if it is really needed.
My presence strengthens each link in the chain,
certain times that you use me, it may be in vain.
In the show it is very creatively related to real life events hence the chain reference. Certain times it has gone in vain to use the TARDIS
Storms when you're older and peace as a child,
with us two together, adventures are wild.
There have been many wild adventures with the TARDIS, I'll provide the storm and peace explanation when I get it(Probably as the time passes.)
A limited spectrum between ceiling and floor,
Shot full of holes from twelve until four.
The TARDIS is small on the outside and bigger on the inside, hence the limited spectrum reference.
In solving this riddle you're just out Of Time,
you should hear my voice as it is sublime.
The "out Of Time" phrase just makes me think about the TARDIS again. The sound it makes when it arrives is indeed sublime and provides hope to the people who hear it.
It should be clear by now that I'm not a Paid Genius Poet,
"What am I, I ask?," by now you should know it.
You are not a paid genius poet and the biggest question on the series is "Doctor Who?"