Google officially stopped providing major updates and security patches for Android 4.2.2 several years ago. Consequently, the ecosystem surrounding this version has stagnated.
. You must find an APK for Play Services specifically built for Android 4.2.2 (API 17) play storeapk for android 422 work
(Version 4.2.42 is a known stable legacy release) play storeapk for android 422 work