Unfortunately, AI illustrations are not that advanced yet and they can't generate the same character in different settings. However, you can achieve some level of consistency by:
Providing very detailed text prompts: "a boy with light-brown hair playing with a gray kitten on a porch of a log cabin in the woods, watercolor illustration" would work a lot better than "a boy playing with a kitten".
Being consistent in your text prompts. The more similar they are, the better.
Specifying the technique you'd like the image to be done with (realistic, watercolor, pastel, cartoon, etc.)
Specifying the colors you'd like in the images.
Try adding "digital art" to the text prompt.
Keep in mind that you'll have to always enter the style, technique and details in every AI text prompt so that the results are as consistent as possible.