For an Android 4.1 device, the version of Google Play Services it requires is vastly different from what a modern Android 14 device uses. You cannot simply take the latest APK file and install it on Jelly Bean; the code is incompatible.
Google Play Services version , released in August 2021, is the final version that officially supports Android 4.1 (Jelly Bean). While existing functionality may continue to work, Google has deprecated support for this OS flavor, meaning no new features or security updates are being developed for it. Understanding Google Play Services on Android 4.1 Google Play Services Apk Android 4.1