The Blue Super Saiyan : The SSJ God Super Saiyan

The Blue Super Saiyan Transformation is a special transformation available only to pure-hearted saiyans and the real name of this transformation is the Super Saiyan God Super Saiyan form.

In fact, this blue SSJ form is reached if a Saiyan character possessing God's powers transforms into a classic Super Saiyan 1.

It is at the same time strange and logical : A Blue flame is hotter than a yellow flame and so the God's powers increase the level of the Saiyan God character so much that when he transforms into a SSJ1, his hairs and aura become blue.

This transformation is seen in the first time in the 2015 Dragon Ball Movie "Fukkatasu No F" aka "Ressurection F" and the only two character who are able to become blue Super Saiyans are Goku and Vegeta (When they fight Golden Freeza).

Like the Battle of Gods movie, the Revival of F movie is cannon which means that the blue SSJ God form aka the Super Saiyan form powered by God's powers is an official transformation for Goku and Vegeta.

How looks like a SSJ God Super Saiyan (SSGSSJG)

Vegeta Blue SSJ God

Vegeta has absorbed God's powers by training with Whis and when he transforms into a Super Saiyan, his hairs become blue like in this video :

Vegeta Blue Super Saiyan VS Goku SSJ God.

Goku Blue SSJ God

When Goku transforms into a Super Saiyan God Super Saiyan or SSGSS, he looks like Super Saiyan 1 with blue hairs and a blue aura.

Goku transforms into a blue SSJ God.