377 Leap Year (1/1)

It would be even better if the leap year date was between March and April since it'd be a great lead up to April Fool's Day. There would always be someone that's confused about how it isn't [Sunday] but still [Saturday] for some reason.

And everyone else would just act as if yesterday didn't exist. The later generations would always be confused, but they'll eventually catch on and continue the tradition.