I wrote down many sentences from a Chinese-dictionary many years ago. I wanted to learn how to use words and phrases. One of the word is pidgin. In it it says "that's not my pidgin"= none of my business.
The phrase "not my pigeon" exists in BrE (although it sounds rather old fashioned to me) to mean not within my area of interest or responsibility, but it is not at all widespread.
I was rather surprised to read in OED that it was originally "not my pidgin", with quotes from 1902 and 1904, and clearly derives from "pidgin" = "business", which OED lists as archaic. All later quotes use the spelling "pigeon". "My" can be replaced with a different pronoun or a person's name.