Medical Expense Subsidy System for Infants and Children in Compulsory Education

I would like to know about the medical expenses system for children.
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.
When I went to a medical institution outside of Tokyo, I couldn't use my medical certificate for infants and children in compulsory education. I would like to know how to claim the medical expenses subsidy.

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