I would like to know how to apply for child allowance when I move to Inagi City or when a child is born.

As a general rule, children's allowances are paid for the month following the month in which the application was made, so please apply as soon as possible.
If the date of birth or the date of moving in is close to the end of the month, even if the date of application is the following month, from the day after the date of occurrence of the reason (in the case of moving in, the scheduled date of moving out submitted by the previous municipality, in the case of birth, the date of birth) If it is within 15 days, it will be paid from the application month.
Please note that if your application is delayed, you will not be able to receive the allowance for the delayed month.
Please check the child allowance (national system) page for details such as required documents.