I really want to buy a hat, but my mother says it’s useless and won’t let me buy it.

Mom probably doesn’t make sense here, as she said “it’s not necessary.” Just save up and buy it yourself! Pocket money, breakfast money, money given by your parents when they are in a good mood, or money from selling scraps, or New Year's money, you can buy whatever you want with this money, or you can directly ask them to give it to you for your birthday.

If it is helpful, please adopt or praise it in time.

Thanks!