There is a stray Himalayan cat that lives under our shed and I know I am responsible for a cat but my parents won't let me keep it I am 13 years old?

The cat is obviously homeless. But just to make sure, remember to check if it has a collar. Is it scared of you? Start to build some trust between you and the cat. This helps. Feed it and it will be more friendly to you. Give it milk,pet it, etc. Your parents need proof that you have enough responsibility for a pet. So, after you have gained it's trust, start taking care of it. Feed it every day (tuna, buy some dry cat food, borrow some from your neighbors.... be creative!) and buy it cat toys (or make some- a feather, a tin foil ball on a string). Spend time with it out by the shed. If it follows you around, you know that now it likes you and trusts you (make sure that it doesn't just like you because you are giving it food, though). After a while, talk to your parents about having a pet again (not in a week, give it a month or two). Bring up that it trusts you and you have been using your own money/resources to take care of it, and that you have been giving it your care and time. Good Luck!