Hello Phillop,
as Adam correctly suggested, you can use the WHERE condition of mentioned API method.
GetChildCategoriesInternal(Int32, String, String, Int32, String, Int32)
Parameters:
categoryId (Int32) - ID of the category to get child categories for.
where (String) - Where condition.
orderBy (String) - Order by expression.
topN (Int32) - Number of records to be selected.
columns (String) - Columns to be selected.
siteId (Int32) - Site ID.
Best regards, Martin