One possible main antagonist could be a rogue ninja who was once an apprentice of Orochimaru and is jealous of Naruto's connection to the Sannin. This ninja might want to steal Naruto's new - found powers related to the Sannin. Another could be a hidden organization that sees Naruto as a threat because of his potential with the Sannin's abilities. They fear he will disrupt their plans for power in the ninja world.
Perhaps a group of dark - arts practitioners who think that the Sannin's combined knowledge in Naruto is an abomination. They want to destroy Naruto to prevent what they see as a perversion of the ninja arts. They might be a cult - like group that has been in the shadows for a long time, and Naruto's existence as the son of the Sannin is the catalyst for them to come out and try to end him.
It could be an ancient evil that was sealed away by the Sannin long ago. Now that Naruto is the son of the Sannin (in the fanfiction), it senses his growing power and awakens. This antagonist would have powers and knowledge from a bygone era and would be a formidable foe for Naruto. It could also be a powerful shinobi from another village who believes that Naruto having the Sannin's legacy gives Konoha an unfair advantage, so he sets out to eliminate Naruto.