The most common and most likely answer to this crossword clue is the 4 letter word SETH
I've seen this crossword clue in The Guardian
S
E
T
H
More clues leading to the result SETH
- Primarily: son
- One of the first people named in Somerset House?
- Novelist; his older brothers fell out fatally
- Adam’s son contributes to Genesis ethos
- Third child registered in Somerset House
- Early man, firm and hard
- Injected into moose, the seed of Adam
- In disguise, the Fourth Man
- Fourth man went down hard
- Fourth man group hated at first
Buddy explains!

The straight part
We know that "seed of Adam" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case seed of adam = seth.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.