Do you use a covered litter box? Covered litter boxes are generally disliked by cats and can lead to litter box avoidance.
Spaying usually helps with middening and spraying outside the litter box. However, if it has become a habit the chances that spaying will help can go down.
Is your kitten declawed? Declawing can make the paws extra sensitive to some types of litter, resulting in pain when using the box. This can cause box avoidance as well. If your kitten is declawed, you could try using a different type of litter. Most "natural" (corn, wheat, walnut, etc) litters are easier on a declawed cat's paws.
If the kitten is not declawed, and has an uncovered box, you could try "retraining" your kitten to use the box. Basically, this involves confining the spaces the cat is allowed to a small room (such as a bathroom) with access to the litter box and everything else the kitten needs. Eventually she should re-learn to use the box. As the box becomes more frequently used you can expand the area she has access to gradually as you see she's using the box.
You could also try using loose soil or sand in the litter box, as some kittens are naturally more inclined to prefer those kinds of textures. As the kitten gets into a habit of using the box, you can gradually replace the soil or sand with regular litter.