We present the largest to date sample of hydrogen Lyman continuum (LyC) emitting galaxy candidates at any redshift, with 18 Lyman {alpha} emitters (LAEs) and seven Lyman break galaxies (LBGs), obtained from the SSA22 field with Subaru/Suprime-Cam. The sample is based on the 159 LAEs and 136 LBGs observed in the field, all with spectroscopically confirmed redshifts, and these LyC candidates are selected as galaxies with counterparts in a narrow-band filter image which traces LyC at z>=3.06. Many LyC candidates show a spatial offset between the rest-frame non-ionizing ultraviolet (UV) detection and the LyC-emitting substructure or between the Ly{alpha} emission and LyC. The possibility of foreground contamination complicates the analysis of the nature of LyC emitters, although statistically it is highly unlikely that all candidates in our sample are contaminated by foreground sources. Many viable LyC LAE candidates have flux density ratios inconsistent with standard models, while also having too blue UV slopes to be foreground contaminants. Stacking reveals no significant LyC detection, suggesting that there is a dearth of objects with marginal LyC signal strength, perhaps due to a bimodality in the LyC emission. The foreground contamination corrected 3{sigma} upper limits of the observed average flux density ratios are fLyC/fUV < 0.08 from stacking LAEs and f_LyC_/f_UV_<0.02 from stacking LBGs. There is a sign of a positive correlation between LyC and Ly{alpha}, suggesting that both types of photons escape via a similar mechanism. The LyC detection rate among protocluster LBGs is seemingly lower compared to the field.