TRENTON — A New Jersey couple that gave their three kids Nazi-inspired names should not regain custody, a state appeals court ruled yesterday, citing a “risk of serious injury” to the children.

The state removed Heath and Deborah Campbell’s youngsters from their home in January 2009. A month earlier, a supermarket had refused to decorate a birthday cake for little Adolf Hitler Campbell.

He and his sisters, JoyceLynn Aryan Nation Campbell and Honszlynn Hinler Jeannie Campbell, have been in foster care ever since.