In the time period you are talking about K, illegitimate children were quite rare, even among the aristocracy. This goes for both the Tudor & the early Stuart periods, when birth rates in & outside marriage were lower than usually imagined. Age at marriage was on average approx mid twenties, which may explain less births. It is not until later, late 17th, 18th century, that things become more profligate.
Also, is there any evidence for an illegitimate child?