Android 4.4.2 (KitKat) is ancient (released 2013). Google officially stopped supporting Play Services updates for KitKat around 2021-2023.
If you try to install a brand new APK, it will likely crash or not install (error -505 or "Parse Error").
The "hot" method means: finding the very last compatible version and side-loading it before your phone dies.
If your device is not automatically updating to the last supported version, you can manually install the APK from trusted repositories: Google Play services (Android 4.4+) APKs - APKMirror
We recommend using this update only for non-critical devices (e.g., a dedicated music player, baby monitor, or GPS dashboard). Do not use a KitKat device for mobile banking or email containing sensitive documents.
This is the most annoying error on KitKat.