there are a lot of solutions here :
http://forums.androidcentral.com/sa...google-servers-try-again-later-galaxy-s3.html
method 1 :
Go to Settings > Security > Check Unknown sources
Head over to apkmirror (apkmirror dot com /apk/google-inc/google-play-services) **I can't post links so you can figure that part out** and get the version of Google Play Services that is applicable to the version of Android that you have on your device.
method 2 :
1. Remove your google account.
2. Download root explorer apk by googling it and install it to your device.
3. Open root explorer first mount it as read and write (you can see the mount option from root explorer main window clearly) and move on to
this directory (system>etc>long press hosts and select "open in text editor ")
4. Then erase everything there and type following .
127.0.0.1 localhost
#127.185.66.4 android.clients.google.com
5. Save it and by touching 3 dots on top right corner then save and exit
6. Now if u have not google play services installed (You can check it in settings>Application manager) then download apk by
googling(Google play services apk for android 4.4/5.0 or for whatever version you are on) .
7.Once installed simply go to settings>add account>google account and you will be able sign in normally.And wont receive any error
messages.