Mark’s son having game with mother (6)
I believe the answer is:
stigma
'mark's' is the definition.
(synonyms)
'son having game with mother' is the wordplay.
'son' becomes 's' (genealogical abbreviation for son).
'having' is a charade indicator (letters next to each other).
'game' becomes 'tig' (I've seen this in other clues).
'with' means one lot of letters go next to another.
'mother' becomes 'ma' (Ma is another word for mother or mum).
's'+'tig'+'ma'='STIGMA'
(Other definitions for stigma that I've seen before include "Mark of infamy or disgrace" , "Part of a flower" , "Mark of shame, stain on reputation" , "Brand or mark of infamy" , "evidence of nastiness?" .)