  Recently, the creation of photonic Landau levels in a twisted cavity has been
demonstrated in Nature \textbf{534}, 671 (2016). Here we propose a scheme to
adiabatically transfer flux quanta in multiples of $3\hbar$ simultaneously to
all cavity photons by coupling the photons through flux-threaded cones present
in such cavity setup. The flux transfer is achieved using external light fields
with orbital angular momentum and a near-resonant dense atomic medium as
mediator. Furthermore, coupling the cavity fields to a Rydberg state in a
configuration supporting electromagnetically induced transparency, fractional
quantum Hall states can be prepared. To this end a growing protocol is used
consisting of a sequence of flux insertion and subsequent single-photon
insertion steps. We discuss specifically the growing of the $\nu=1/2$ bosonic
Laughlin state, where we first repeat the flux insertion twice creating a
double quasi-hole excitation. Then, the hole is refilled using a coherent pump
and the Rydberg blockade.
