Your kitten is litter trained not newspaper trained.
Please ring the people you got it from and ask what kind of litter they used and get that. Once it is back to using its litter you might be able to introduce paper by putting it under the litter and gradually reducing the amount of litter but cats like to dig when they do their dirty cat business and bury it so newspaper goes against that. Your kitten is probably pretty distressed about the paper because cat's are quite fastidious animals.
TBH I don't fancy the idea of getting your cat to do it outside - it is smelly and with children about they're likely to step in it (or worse if you have a toddler who likes to eat random stuff). I prefer it in a litter box where I can put it in a child proofed room and flush it away instead of leaving it hanging about in the garden.