  We have investigated the signal for physics beyond the Standard Model via
Higgs plus photon final state, hitherto unobserved at the LHC, in the framework
of Standard Model Effective Field Theory. Using the relevant dimension-6
operators, we probe two distinct classes of interactions, based on the Lorentz
structure of Higgs couplings to gauge bosons and fermions. To begin with,
constraints on the Wilson coefficients of these operators have been derived
from existing experimental data. We then focus on the hadronic decay of the
Higgs boson to two bottom quarks in the boosted regime, leading to a high $p_T$
fat-jet recoiling against a hard photon. Following a CMS Run II search for a
resonance decaying into a Higgs boson and a photon, a detailed signal and
background analysis for this channel has been done and limits on the relevant
Wilson coefficients have been obtained. By performing a cut-based analysis, we
identify some kinematic observables that distinguish between signal and SM
background. Minimum values of the Wilson coefficients that will yield $3\sigma$
signal significance at the 14 TeV run of the LHC with $3000 ~\rm fb^{-1}$ data,
have been obtained. A multivariate analysis using a boosted decision tree and
exploiting the jet substructure techniques further help to isolate the regions
of phase space where the contribution of SMEFT driven signal is significantly
enhanced. Finally, we briefly discuss the parameter dependencies and
interpretations of the allowed values of the coefficients on a particularly
interesting UV complete model namely, Minimal Supersymmetric Standard Model.
