Boyzarro was created by Patrick Gleason and Peter J. Tomasi. He made his first appearance in Superman #42 - Bizarroverse Part 1: Father of Boyzarro.
The beginning of the issue is very much like the first issue of Gleason/Tomasi's run of Superman. We see Bizarro working on the ranch, mourning the dead of someone, greeting his son and so on and so forth. However, there's one huge discrepancy, which is the language (they say the opposite of what they mean) and the body language ("thumbs down", while he actually means "thumbs up") are poles apart from what we are used to. This can lead to quite some confusion.
Jon and Kathy visit Bizarro world. Jon is amazed by how much Boyzarro, sort of resembles him, it’s like looking in a cracked mirror. Jon and Kathey quickly leave before their parents would start getting suspicious. Boyzarro manages to leave Bizarro world and travel together with Jon and Kathy.
Jon inititally is in shock, but over the course of a few days the two of them bond together and even help Superman. It’s all fun, but nothing lasts forever, Boyzarro has to go to his home planet. Superman, Jon and Boyzarro find a way back to Bizarro world.
Bizarro’s response to Clark is rather unpleasant, as he’s firm that it was Clark himself who’d kidnapped Bizarro’s son. This is of course not the case, since Boyzarro left on his own will. After a huge clash between Superman and Bizarro, Superman manages to talk some sense into Bizarro that they are in fact on the same page when it comes to family. Bizarro world, or Aerth, is collapsing and there’s only one pod left. Bizarro uses the pod and refuses to let Boyzarro join. Saddened by the fact that his own dad wouldn’t rescue him, it seems that he’s going to die. Fortunately, Superman and Jon rescue him and together they travel back to earth. From now on, Boyzarro lives on planet earth.