Even with the official package, old Android versions present challenges. Here are real-world fixes:
Your system partition is full. Fix: Use a smaller Gapps variant. For 4.2.2, choose “pico” or “nano” from OpenGapps (only Play Store and core services). Remove unused system apps via a root uninstaller before flashing. Official Gapps For Android 4.2.2 Jellybean Flashable.zip
If you are performing a fresh ROM install, perform a "Factory Reset" wipe. If you are just adding GApps to an existing ROM, wipe the Dalvik and Cache partitions. Even with the official package, old Android versions