While it isn’t possible to change the system font on your iPhone you can install third-party apps such as Font Diner and Fontix which allow you to use different fonts in some of your apps.
Apple’s own apps, such as Mail, support native font changes and you can access the font library by going to Settings, General, and Fonts.
To add new fonts to your library you need to install a third-party app, browse the available font sets, tap on Activate, press Agree, and finally, press Install.
If you want to change fonts in messaging apps you will need to install a third-party keyboard app such as Fontix.
This app will completely change your keyboard but you can switch between keyboards easily on your iPhone.
Once you’ve installed the app, navigate to Settings, Apps, Fontix, and Keyboards, toggle on Fontix and Allow Full Access, open a chat app, bring up the keyboard, tap on the globe icon to change keyboards until you find the Fontix keyboard, swipe through the font options, and select your favorite.