Look for Google Play Store versions around v15.2.23 or v25.2.22 , as some of these were the last to support the "Jelly Bean" API level 17.
Google has officially deprecated support for versions 4.0.3 and earlier, and 4.2.2 is currently in a "legacy" state where most Google services (Gmail, YouTube, Play Store) will no longer sign in or sync. How to Attempt an Update/Install google play store for android 4.2.2 apk
When searching on these sites, look for Google Play Store (Android TV) or Google Play Store (Wear OS) if you are on a specific device, but for phones, look for the standard "Google Play Store" listings. Scroll down to find a version released around 2015 or 2016 . Look for Google Play Store versions around v15
If you're not comfortable downloading and installing an older version of the Google Play Store APK, there are alternative app stores available for Android devices: Scroll down to find a version released around 2015 or 2016