I would like to know how to apply for a medical certificate for infants and children attending compulsory education when I move to Inagi City or when a child is born.

As a general rule, the start date of eligibility will be the first day of the month in which the application was made, so please complete the procedure 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 one month, you will be eligible to receive benefits retroactively to the day you were born or moved in.
Please note that if the application is delayed, the medical expenses for the delayed month will not be covered by the subsidy.
For details, such as required documents, please check the Medical Expense Subsidy Program for Infants for preschool children, and the Medical Expense Subsidy Program for Compulsory Education Children for elementary and junior high school children.