1. Where are you trying to Register the database with server: In ArcCatalog or from Server Manager..?
From ArcCatalog
2. Which version of ArcGIS and PostgreSQL are you working with?
ArcGIS 10.2
PostgreSQL 9.6.1 in local
PostgreSQL 9.3.15 in server
3. Is this a new installation and are you trying for the first time to register a database with server on this?
Yes
I am going to update the version of PostgreSQL to 9.6.1 in the server and try again.