But really, what is the point? Yes, a child added to the family 15 years after the last one, when there is a daughter of childbearing age *might* be an illegitimate child. Or, it might be one of nature's little tricks on older parents. You can't tell without DNA, so what good does it do to speculate?
If you want to get gossipy, why not look at, say, a child born less than 12 months after another one? It could be another woman's, say a sister's child, brought in to save face. Or the father had an affair, and wants his child brought up with his family. It's all possible. And it's probably true a certain percentage of the time. But speculating on what's possible isn't particularly helpful, unless you get a thrill out of thinking that people in other generations might have been naughty.
Actually, any child at all might not be the legitimate offspring of both its legal parents. So, we can look at every single child in the family tree as potentially illegitimate, but it doesn't really seem nice to do so.