You can't install an APK on iPhone: it's Android's app format, and "APK installers" for iOS don't work. What you need is the app's iPhone version. If Apple rejected it from the App Store, look for it on Aptoide, in the EU, Japan and Brazil.
Why APK files don't run on iPhone
APK is Android's app format, built for Android only. iPhone uses its own format and system, so no setting or trick makes it open an APK.
Sites that promise an "APK installer for iOS" don't work: at best they show ads, at worst they push you to install something you didn't want. Running Android inside a PC emulator such as UTM SE is technically possible, but iOS keeps emulators slow, so Android apps barely respond.
What you really need: the iPhone version
An app with the same name on Android and iPhone is really two versions made by the same developer. If you can't find the iPhone version on the App Store, there are usually two reasons: the developer never made one, or Apple's App Store review rejected it.
The second case is more common than people think. Apps that Apple doesn't allow, from downloaders to emulators to apps with their own payment systems, often exist only as APKs for exactly that reason.
Get the iPhone version on Aptoide
In the EU, Japan and Brazil, developers can publish the iPhone versions Apple rejected on Aptoide, without App Store review. Apple still notarizes every app, so it's safe to install, and you don't need to jailbreak.
If an app you know from Android is missing from the App Store, Aptoide is the first place to look.
- Open aptoide.com/ios in Safari on your iPhone.
- Tap Install and allow Aptoide as a marketplace when iOS asks.
- Search Aptoide for the app you found as an APK.
For Android games: play in the cloud
If what you wanted was an Android game, Aptoide's Play on the Cloud streams selected games to your iPhone. The game runs on a server, so there's nothing to install.