Start a blog. Blogging is how I make a living and just a few years ago I never thought it would be possible. I made over $320,000 in 2015 by blogging and nearly $1,000,000 in 2016. You can create your own blog here with my easy-to-use tutorial. You can start your blog for as low as $2.95 per month plus you get a free domain if you sign-up through my tutorial.
Ask your parents if they'll pay you for doing more chores. You're probably already expected to do chores around the house and help out your family for free. If you need a little extra pocket change, however, ask your parents if there's something else you can do for a small fee. For instance, maybe your mom really hates folding laundry and would be willing to pay $5 a week for you to do it instead. Whatever it is, let your parents know you're willing to take on more work for a bit of allowance.
If you have a good idea for an app, and the skills to create it, then producing your own premium app can be profitable. However, with so many free apps available, it may be hard to convince people to pay. If you want to go down the premium app route, consider having a basic free version to encourage people to download the app in the first place. You can then provide the option of upgrading to a premium plan once users realize how useful the app is.