I've searched quite a bit for this but surprisingly could not find any comprehensive answer. XCode doesn't provide any simple way to add dropdown lists to iOS interfaces. Stackoverflow just showed workarounds and long code just to get a simple dropdown list. This leads me to believe that the design pattern is to not really use dropdown lists! Is this true? And if so, what is the recommended alternative?
iOS makes it much easier to use "Pickers". These may work depending on what you need the "Dropdown" to do. See new link https://developer.apple.com/ios/human-interface-guidelines/controls/pickers/
Even though Apple recommended (and surprisingly still recommends) pickers for dropdowns, not even they use it anymore. Spoilers:
In both these cases, the "logic" would dictate to use a dropdown + picker. Apple chose a much better solution for their own apps.
Still, a whole screen to pick between "Female" or "Male" (pardon the binary example) seems exaggerated. Personally, I believe the best option is to design what visually looks like a dropdown element that, when tapped, opens an Action Sheet:
The reasoning is that an action sheet is better than a picker because:
1) Action Sheets do not require scrolling to read and/or choose options that are not highlighted;
2) Action Sheets dim the background, providing clear affordance that by clicking outside the action sheet other elements will not be activated (whereas a picker makes the user unsure of where to tap in order to close the picker without accidentally tapping something else);
3) Action Sheets have "Cancel" buttons;
4) Action Sheets items are 44 points high, have margins between buttons and can list more options using more space on the screen;
Action Sheets are also better than the fullscreen listed beforehand, because they don't take the user to another screen, and thus making the flow more... fluid; and they're better than a custom-built alternative because they're native and consequently "more future-proof". Brad Frost would probably correct me, saying they're actually "future-friendly".
By the way, Luke Wroblewski has an excellent article on why dropdowns should be the UI of last resort, and these 4 very excellent videos going into details as to when and why one element works better than the other (and with research to back it up):
Put your headphones and dive in. The videos are worth it.
Why do you need a dropdown on iOS? Dropdowns are incredibly hard to interact with on mobile (iOS or Android). I'd suggest an alternative pattern like a picker or as Paul mentioned, Drill Down Lists (a series of Table views, for multiple selection)