Sounds like the kitty litter tray is too small. Cats naturally like to cover up their faeces, and will dig and push dirt or kitty litter to cover it. It doesn't sound like she has much room to do this. She could be getting faeces on her paws attempting to cover it, or just by trying to exit the litter box.
I suspect a rectangular shape may be easier for your kitten to use, than a round shape.
Go for a minimum size or 345 mm wide x 440 mm high x 125 mm deep.
Cats are pretty clean creatures and she wouldn't like having faeces on her front paws. Most importantly, be patient with her and gently clean her paws with a damp warm cloth. She cannot help that this is happening. It's always the humans who are responsible for their pets behaviours.
The other issue is also to consider, her stools may be too runny. Either way, she needs a bigger litter box.
Here are some useful posts to help you get started:
How often should a litter box be cleaned?
How can I reduce litter/waste odor?
Cat digs litter out of the box
What types of kitty litter are there and what else can be used as kitty litter?