Anatidaephobia is the fear of being watched by ducks. And despite this existing as a fun fact for decades, it may not actually be a real thing. If it is, it originated in an awfully strange place for a real phobia. Well here is the actual origin:
Ducks are probably only watching you if you get too close to them or their nests. But we don’t want to downplay phobias, because they’re very real and produce real physical symptoms. So, could someone fear that a duck is watching them? Sure.
The question is whether this fear rises to the level of anatidaephobia. That’s less likely since the word was coined by Gary Larson in his comic The Far Side. The idea of this particular phobia is a hoax.