What is the way to atone for registering a fictitious newborn in official records to obtain material and administrative privileges, and then deleting him after repentance?

The question is unclear, but if the intention is to defraud in order to register a newborn or receive a newborn grant, then this is impermissible. To absolve oneself from the deception involved in an unlawfully obtained newborn grant, it must be returned to the entity from which it was taken, if possible, unless they absolve you. If you are unable to return it, then donate it to the poor and needy.