  We present general one-loop contributions to the decay processes
$H\rightarrow f\bar{f}\gamma$ including all possible the exchange of the
additional heavy vector gauge bosons, heavy fermions, and charged (also
neutral) scalar particles in the loop diagrams. As a result, the analytic
results are valid in a wide class of beyond the standard models. Analytic
formulas for the form factors are expressed in terms of Passarino-Veltman
functions in the standard notations of {\tt LoopTools}. Hence, the decay rates
can be computed numerically by using this package. The computations are then
applied to the cases of the standard model, $U(1)_{B-L}$ extension of the
standard model as well as two Higgs doublet model. Phenomenological results of
the decay processes for all the above models are studied. We observe that the
effects of new physics are sizable contributions and these can be probed at
future colliders.
