Who wrote the poem peter piper?

It is a Mother Goose Rhyme.

Mother Goose is a well-known figure in the literature of Fairy Tales and nursery rhymes. She is often prominent in Mother Goose stories, also more commonly known as "nursery rhymes"

Here are just a FEW of the many related to Mother Goose.

All Around the Mulberry Bush

An Apple A Day

The Ants Go Marching

As I Was Going to St. Ives

As I Went To Bonner

Baa, Baa, Black Sheep

Barber, Barber, Shave a Pig

Bat, Bat, Come Under My Hat

Bell Horses

Birds of a Feather

Bobby Shaftoe