  In recent years, a number of Lyman continuum (LyC) leaker candidates at
intermediate redshifts have been found, providing insight into how the Universe
was reionised at early cosmic times. Here we identify new LyC leaker candidates
at $z\approx 3-4.5$ and compare them to objects from the literature to get an
overview of the different observed escape fractions and their relation to the
properties of the Lyman $\alpha$ (Ly$\alpha$) emission line. The aim of this
work is to test indicators for LyC leakage and to improve our understanding of
the kind of galaxies from which LyC radiation can escape. We use data from the
Hubble Deep Ultraviolet (HDUV) legacy survey to search for LyC emission based
on a sample of $\approx 2000$ Ly$\alpha$ emitters (LAEs) detected previously in
two surveys with the Multi-Unit Spectroscopic Explorer (MUSE), MUSE-Deep and
MUSE-Wide. Based on their known redshifts and positions, we look for potential
LyC leakage in the WFC3/UVIS F336W band of the HDUV. The escape fractions are
measured and compared based on spectral energy distribution (SED) fitting
performed using the CIGALE software. We add twelve objects to the sample of
known LyC leaker candidates, one of which was previously known, and compare
their Ly$\alpha$ properties to their escape fractions. We find escape fractions
between $\sim 20\%$ and $\sim 90\%$, assuming a high transmission in the
intergalactic medium (IGM). We show a method to use the number of LyC leaker
candidates we find to infer the underlying average escape fraction of galaxies,
which is $\approx 12\%$. Based on their Ly$\alpha$ properties, we conclude that
LyC leakers are not very different from other high-z LAEs and suggest that most
LAEs could be leaking LyC even if this can not always be detected due to the
direction of emission and the transmission properties of the IGM.
