Hello. First you step explanation of how to synchronize contacts so you can see if you've made a mistake. Secondly I mention some tips to resolve errors.
Instructions to sync your contacts with your device:
Open the Settings application on your device.
Select Mail, Contacts, Calendar.
Select Add Account ...
Select Other.
Select Add CardDAV account.
Write the details of your account in the following fields:
Server: type "google.com".
User: enter your full email address of your Google Account or Google Apps.
Password: Enter the password for your Google Account or Google Apps. (If you've enabled two-step verification, you have to create and introduce a specific application password).
Description: Write a description of the account ("Personal Contacts", for ex.).
Select Next (at the top of the screen).
Check the "Contacts" is checked.
When you finish the settings, open the Contacts application on your device and synchronization will start automatically.
If you have any problems, do the following:
Open CardDAV account you created in Settings> Mail, Contacts, Calendar, in the "Accounts" section. Confirm that the account is enabled.
If the account is activated, select Advanced at the bottom of the page and verify that the Use SSL option is enabled.
If you've changed something, click the Done (in the upper right of the screen settings on your account) to save changes button.
If you are still having difficulty syncing your contacts with CardDAV, log in to your Google account on the web. You may receive a message because it is a "Start Location unusual session."
I hope this information will help you.
A greeting!