Starting in 2021, Google began phasing out support for Android KitKat (API level 19-20). The last official version of Google Play Services that fully supports Android 4.4.2 is from the or 22.x.x series. Newer versions (23.x.x and above) require Android 5.0 (Lollipop) or higher.
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APKMirror is the most reliable source for clean, signed, original APKs from Google. They verify cryptographic signatures. Starting in 2021, Google began phasing out support