To help find the exact file for your phone, tell me your and your device's processor architecture (like ARM64 or ARM). I can also help you find a direct download source or walk you through fixing specific error codes you are seeing.
This version is particularly crucial for devices running Android Marshmallow (API 23) or Nougat (API 24) that may not be receiving official OTA updates from manufacturers. Why Update to Google Play Services 13278? google play services 13278 ultima version link