US censuses between 1850 and 1870 list every name in a household, but bear in mind that not all children are children of the head of the household. They may be step-children, foster children, nieces, nephews, other relatives, etc. Even in the 1880 and later census where relationships to the head of household are given, “children” of the head of the household may not necessarily be their children.
Use the census as a starting point to other records suggested by the enumeration, particularly vital records, property records, military records, etc.
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