You could start by talking to your parents or guardians. Explain to them why you're interested in young adult fiction, like how it can expand your vocabulary and understanding of different perspectives. They might be more likely to give you permission if they know it has educational value.
Ask your teacher. If it's for a school - related activity, such as a book club or independent reading project, your teacher can write a note or talk to your parents on your behalf. They can vouch for the quality of the young adult fiction you want to read and assure your parents that it's appropriate for your age and reading level.