Assuming you want the two best APK sources/versions of Google Play Services compatible with Android 4.2 (API level 17) and guidance on installing them safely, here are concise recommendations and steps.
Would you like help identifying your device’s architecture (ARM/ARM64/x86) or DPI to pick the exact correct APK variant? google play services apk for android 42 2 best
Authentication Errors: You won't be able to sign into your Google Account. Assuming you want the two best APK sources/versions