  We study the observability of non-standard top Yukawa couplings in the
$pp\rightarrow t(\rightarrow \ell \nu_\ell b ) h(\rightarrow \gamma\gamma)j$
channel at 14 TeV high-luminosity LHC (HL-LHC). The small diphoton branching
ratio is enhanced when the $\mathcal{CP}$-violating phase, $\xi$, of the
top-Higgs interaction is non-zero. When the modulus of the top-Higgs
interaction assumes the SM value, $y_t=y_t^{SM}$, we find that the signal
significance reaches $2.7\sigma$ $( 7.7\sigma)$ when $\xi= 0.25\pi$ $(0.5\pi)
$. Furthermore, the different couplings modify the polarisation of the top
quark, and can subsequently be distinguished via asymmetries in spin
correlations with the final state leptons. The diphoton decay mode is found to
be significantly more promising than the previously considered $pp\rightarrow
t(\rightarrow \ell \nu_\ell b ) h(\rightarrow b\overline{b})j$ channel.
