  The recent searches for z>11 galaxies using the James Webb Space Telescope
have resulted in an unexpectedly high number of candidate objects, which imply
at least an order of magnitude higher number density of z>11 galaxies than the
previously favored predictions. A question has risen whether there are some new
types of contaminants among these candidates. The candidate sample of Yan et
al. (2023a), totalling 87 dropouts, is the largest one, and we notice that a
number of these candidates are point-like. We hypothesize that the point-source
dropouts could be supernovae at high redshifts. Further investigation shows
that most of their spectral energy distributions indeed can be explained by
supernovae at various redshifts from z ~ 1--15, which lends support to this
hypothesis. Attributing such point-source dropouts to supernova contamination
cannot eliminate the tension, however, because they only account for ~10% of
the Yan et al.'s sample. On the other hand, the discovery of "contaminant"
supernovae at z>3 will have a series of important implications. Ironically, the
existence of supernovae at $z>10$ would still imply that the previously favored
picture of early galaxy formation severely underestimates the global star
formation rate density such redshifts. Multiple-epoch JWST imaging will be the
simplest and yet the most efficient way to further test this hypothesis.
