  We present a systematic search of candidate galaxies at z > 11.3 using the
public Near Infrared Camera data taken by the James Webb Space Telescope (JWST)
in its Cycle 1, which include six blank fields totalling 386 sq.arcmin and two
lensing cluster fields totalling 48 sq.arcmin. The candidates are selected as
F150W, F200W and F277W dropouts, which correspond to z ~ 12.7 (11.3 < z <
15.4), 17.3 (15.4 < z < 21.8) and 24.7 (21.8 < z < 28.3), respectively. Our
sample consists of 123 F150W dropouts, 52 F200W dropouts and 32 F277W dropouts,
which is the largest candidate galaxy sample probing the highest redshift range
to date. The F150W and F200W dropouts have sufficient photometric information
that allows contaminant rejection, which we do by fitting to their spectrum
energy distributions. Based on the purified samples of F150W and F200W
dropouts, we derive galaxy luminosity functions at z ~ 12.7 and 17.3,
respectively. We find that both are better described by power law than
Schechter function and that there is only a marginal evolution (a factor of <
2) between the two epochs. The emergence of galaxy population at z ~ 17.3 or
earlier is consistent with the suggestion of an early cosmic hydrogen
reionization and is not necessarily a crisis of the LCDM paradigm. To establish
a new picture of galaxy formation in the early universe, we will need both JWST
spectroscopic confirmation of bright candidates such as those in our sample and
deeper surveys to further constrain the faint-end of the luminosity function at
M > -18 mag.
