"On my ones" is a popular phrase used in South East London high schools and is simply slang for “on my own”. As all slang does, the phrase slowly died out and is now used purely for comic effect. Variants of the phrase include: On your ones, Ones and One-sies.
Guy A: I'm just going to go get some chocolate.
Guy B: Don't leave me On my ones!
Guy A: Shut up...