These are phrases that have been used in English since the 14th century with the following meanings:
son of Adam (also Adam’s son): a man or boy, esp. one who is weak-willed, fallible, or susceptible to temptation (with reference to Adam's part in the biblical story of the Fall of Man)
daughter of Eve (also Eve’s daughter) literary a girl or woman, esp. (with allusion to Eve's part in the biblical story of the Fall of Man) one who is weak-willed, lascivious, or susceptible to temptation.
Oxford English Dictionary.
“Son of Adam” comes from a mis-translation of Ecclesiastes 3.21 where the Hebrew is “bə-nê hā-’ā-ḏām” (of the sons of men) but the Vulgate translates this as “filiorum Adam” (of the sons of Adam):
Quis novit si spiritus filiorum Adam ascendat sursum, et si spiritus jumentorum descendat deorsum?
Who knows whether the spirit of the sons of Adam goes upwards, and whether the spirit of animals goes downwards?
There is a similar phrase in the apocryphal book of Sirach 40:1 and in both cases Wycliffe’s 1382 English translation (based on the Vulgate) used “sons of Adam”.
“Daughter of Eve” is obviously a parallel formation; the OED’s first citation is from Chaucer’s Canterbury Tales, where one manuscript has
And þouhe þat I þe vnworþe douhter of Eue
Be synful ȝit accept my be-leue.†
Geoffrey Chaucer (c. 1380). Second Nun’s Tale, lines 62–63. British Library Lansdowne 851. In Frederick J. Furnivall (1879). The Lansdowne Ms. of Chaucer’s Canterbury Tales p. 529. Oxford University Press.
† And though that I the unworthy daughter of Eve / Be sinful yet accept my belief.
Other manuscripts of the Canterbury Tales have “son of Eve” instead of “daughter”, and the scansion shows that “son” must have been the original word. But the Lansdowne scribe’s mis-correction to “daughter” shows the attraction of the form of words that matches the gender of the descendant to that of the ancestor.