What is a poetic counterpart? Or how do you write a poem that intertexts with an essay/short story?I need to write a poem that intertexts or is the...

A poetic counterpart is a poem that is based on or inspired by another work of literature or art.  A poetic counterpart to Jack Kerouac's novel On the Road is Alan Ginsberg's "Howl," for example, as as they both are descended from the same Beat generation.

A intertext is a modern re-telling of an older story, novel, or poem.  An example of this is James Joyce's Ulysses, a novel based on Homer's epic.  Richard Wilbur's "Beowulf" is another.  Tim O'Brien's short story "The Man I Killed" is an intertext with Thomas Hardy's "The Man He Killed."

Or, intertextuality is found within the same work.  For example, Beowulf has intertextuality within it.  The original author wrote a very pagan poem only to have it revised by monks who added Christian elements to it.

So, to write a poem simply base it on a short story in terms of major elements.  Keep it similar to the original, but you must make it more modern, spin it to your tastes, make it fit a new reader.  Texts need to be changed, revised, or added to over time.  Intertextuality is a way to overlay a new theme on top of an old story.