  At present, the study of the charm-quark Yukawa coupling at the Large Hadron
Collider mainly restricts the coupling constant $y_c$ through the Higgs decay
channels. Such signal suffers from overwhelming QCD background, and derives
most sensitivity from the $Vh$ associated production channel. In addition,
sensitivity to a possible CP complex term of $y_c$ is lost. We study the $ch$
associated production channel at the HL-LHC and FCC to probe the charm Yukawa
coupling. By making use of the interference contribution among channels, and
machine learning techniques to separate the different contributions,
sensitivity on possible deviation from a standard model charm Yukawa coupling
is derived. Under the $\kappa$ framework, a 1$\sigma$ projected bounds of
$\kappa_c < 5.62$ (HL-LHC) and $-1.52 < \kappa_c < 1.62$ (FCC) are achieved.
When further allowing for CP-structure for the charm Yukawa, and comparing with
other complementary hadron collider signals, we reach projected bounds on the
CP-odd and CP-even components of the charm Yukawa of $-2.46 < \tilde{\kappa_c}
< 2.46$, $ 0.23 < \kappa_c < 1.74$ at the HL-LHC and $-1.05 < \tilde{\kappa_c}
< 1.05$, $ 0.57 < \kappa_c < 1.28$ at the FCC.
