  We consider the emission of a photon by a scalar charged particle in a
constant and uniform magnetic field. In contrast to the conventional approach
with both photon and outgoing charge being assumed to be detected, we study the
case where only the charge is detected and investigate the properties of the
emitted photon. The background magnetic field is taken into account exactly in
the calculations and the charge is described by relativistic Landau states. It
is shown that the emitted photon state represents a twisted Bessel beam with a
total angular momentum given by $\ell-\ell'$, where $\ell$ and $\ell'$ are
angular momentum quantum numbers of the initial and final charged particle,
respectively. The majority of photons emitted by unpolarized charges,
especially in the hard X-ray and $\gamma$-ray range and in critical and
sub-critical magnetic fields, as compared to the Schwinger value of $H_c =
4.4\times 10^9$ T, turn out to be twisted with $\ell-\ell'\gtrsim 1$.
