No. YouTube Music never officially supported KitKat. Use NewPipe or the main YouTube app for music.
If possible, check for a system update to move past KitKat, as many modern apps require at least Android 9.0. Google Help Check for Updates About Device Software Update direct link to a specific legacy version that is confirmed to work? How to Install APK Files on Android Youtube Apk Download Android 4.4 2
None. Google Play Services no longer updates for KitKat, meaning the official YouTube app from the Play Store is incompatible. Youtube Apk Download Android 4.4 2
Finding a working YouTube APK for is difficult because Google has officially ended support for this version. The current YouTube app requires Android 9.0 or higher to run properly. Youtube Apk Download Android 4.4 2