  We report results of a search for galaxies at z>3 with Lyman continuum (LyC)
emission using a narrow-band filter NB359 with Subaru / Suprime-Cam in a ~800
arcmin$^2$ blank field around the GOODS-N. We use 103 star-forming galaxies
(SFGs) and 8 AGNs with spectroscopic redshifts in a range between 3.06 and 3.5,
and 157 photometrically selected z=3.1 Lyman $\alpha$ emitter (LAE) candidates
as the targets. After removing galaxies spectroscopically confirmed to be
contaminated by foreground sources, we found two SFGs and one AGN as candidate
LyC emitting sources among the targets with spectroscopic redshifts. Among LAE
candidates, five sources are detected in the NB359 image, and three among them
may be contaminated by foreground sources. We compare the sample galaxies in
the GOODS-N with those in the SSA22, where a prominent protocluster at z=3.1 is
known and the LyC search using the same NB359 filter has been made. Frequency
of galaxies with LyC leakage in the SSA22 field may be about two times higher
than the galaxies in the GOODS-N with the sample UV magnitude range, although
the numbers of LyC detections in these fields are too small to make a
statistically significant conclusion. By combining the sample galaxies in these
fields, we place the 3$\sigma$ upper limits of the observed LyC-to-UV flux
density ratio and LyC escape fraction for galaxies at z=3.1 with absolute UV
magnitude $M_{UV} < -18.8$ as ($f_{LyC}/f_{UV})_{obs} < 0.036$ and
$f_{esc}^{abs}<8$\%, respectively.
