How to install Google Play Services without through Play Store in Redmi 3? A bunch of my apps ask me to install Google Play Services but my Play Store won't start since the service is missing.
Just install Google Play Services from a trusted website. You can download it from apkmirror.com, but it is important to choose the right version for your smartphone. Read the minimum Android version and architecture (arm/arm64/x86).

After that you need to install the APK. Well, sometimes the Play Services don't work after the installation.

In my experience, it's caused when the Android doesn't have Google Services Framework, Google Contacts Sync, and Google Account Manager app. If your phone doesn't have all the Google apps (usually with MOD ROM or MIUI ROM) you have to install them first. Just find them on the website I mentioned above.