Is there a fuse on an alternator?

no there is not a fuse built into any alternator that i have seen to date (been a mechanic for 10 yrs) HOWEVER most vehicles have a charging fuse located either in-line or at the fuse panel so that if the rectifier or voltage regulator goes out the battery does not receive too much voltage or the wrong type of voltage ac versus dc
in short no the alternator doesn't but the vehicle should have one in the alternator circuit