The etymology of the word was quite interesting:
English borrowed "epigone" from German in the 19th century. The Germans themselves had taken the word from the Latin "epigonus," which means "successor." The Latin term followed the Greek "epigonos," which was often used in plural to designate the sons of seven legendary Greek leaders who were defeated at Thebes. "Epigonos" in turn came from the Greek verb "epigignesthai," meaning "to be born after." "Epi-" can mean "after," and "gignesthai" means "to be born."
While this word has Greek origins and can mean "disciple" the word we see translated as "disciple" in the writings of the Apostles is mathetes.
The interesting link I found was the follower/disciple meaning of this term is related to being born. It reminds me of the words of the Master in John 3 when He speaks of being "born again" and 1 Peter 1 when Peter echoes that thought. John 3 uses the words gennao anothen while 1 Peter uses anagennao.
This idea of "coming after" also reminds me of the words of the Master in Matthew 16:24:
Then Jesus said to His disciples, "If anyone wishes to come after Me, he must deny himself, and take up his cross and follow Me.