Identifying non-contaminated sample of high-redshift galaxies with escaping Lyman continuum (LyC) flux is important for understanding the sources and evolution of cosmic reionization. We present CLAUDS $u$-band photometry of the COSMOS field to probe LyC radiation from spectroscopically confirmed galaxies at $zgeq3.5$ and outside the standard Lyman-break galaxy colour selection expectations. Complementary to the CLAUDS data, we use Subaru multi-filter photometry, textit {Hubble Space Telescope} ($HST$) multi-filter imaging, and the spectroscopic surveys D10K, VUDS and 3D-HST. We present a sample of Lyman continuum galaxy (LCG) candidates in the redshift range $3.5lesssim zlesssim5.1$. Here, we introduce 5 LCG candidates, where two are flagged quality 1 and three quality 2. The estimated $f_{rm esc}^{rm abs}$ for quality 1 candidates are in the range $sim5% - 73%$ and $sim30% - 93%$. These estimates are based on our derived parameters from individual galaxies as inputs to a range of BPASS models as well as mean intergalactic medium (IGM) and maximal intergalactic and circumgalactic media (IGM+CGM) transmission. We conclude that our search for LCGs is most likely biased to lines of sight with low HI densities or free from Lyman limit systems. Our two best LCG candidates have EW (Ly$alpha)leq50$AA and we find no correlation or anti-correlation between EW (Ly$alpha$), $f_{rm esc}^{rm abs}$, and $R_{rm obs}$, the ratio of ionizing to non-ionizing observed flux in the measured passbands. Stacking candidates without solid LyC detections ($S/N<3$) results in an estimated $f_{rm esc}^{rm abs}$ from galaxies not greater than $1%$.
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