Does anyone know if the ArcGIS javascript API version has any dependency on which version ArcGIS is on. I am trying to see the minimum javascript api version that will go with arcgis10.3.
Not a straight 1 to 1 dependency. But some stuff like Query Statistics (at v 2.6) needs ArcGIS Server 10.1 and above since that option to return statistics was on that release.
All versions of the JavaScript API should work fine with 10.3 server.