Nuntium igitur ad navem misit qui Jasoni persuaderet ut sibi auxilium ferret. I understand why ferret has subjunctive form but why is persuaderet in the subjunctive?
To express purpose. “He sent a messenger to persuade Jason,” i.e. in order that he (the messenger) might persuade Jason. It’s the same kind of subjunctive that you’d have with ut introducing a purpose clause, but qui makes it clear that it was the messenger (not the sender) who was to do the persuading.
Think how different the meaning would be if the verb were an indicative. You quite often find subjunctive in relative clauses when it’s not simply a matter of fact.
As mwh said. I think the qui is what threw you off. This is a regular variation of the purpose clause where qui replaces ut. It could be rendered in English thus: "He sent a messenger to the ship, who was to persuade Jason that…