Do not download version 17.x or higher. Those require Android 5.0 (Lollipop) or newer and will crash on KitKat.
While APKPure is excellent, consider these trusted sources for legacy Google Play Services: google play services for android 44 2 apkpure
) and toggle on the option to allow installations from "Unknown Sources". Download the APK : Visit the Google Play Services page on APKPure and download the version specifically compatible with Android 4.4+ : Open the downloaded Do not download version 17