Ben Lederman and Patrice were affected by the FIFA ban in 2014.
Labinot Kabashi, Imad el Kabbou, Anssumane Fati of Cadete B and Xavi Simons can play football again.
The club won't be able to register Arda Turan in place of the injured Rafinha.
Barcelona is confused by the new precautions taken by FIFA regarding the children.
The club claims to have signed them legally.