  The recently introduced topological heavy fermion model (THFM) provides a
means for interpreting the low-energy electronic degrees of freedom of the
magic angle twisted bilayer graphene as hybridization amidst highly dispersing
topological conduction and weakly dispersing localized heavy fermions. In order
to understand the Landau quantization of the ensuing electronic spectrum, a
generalization of THFM to include the magnetic field B is desired, but
currently missing. Here we provide a systematic derivation of the THFM in B and
solve the resulting model to obtain the interacting Hofstadter spectra for
single particle charged excitations. While naive minimal substitution within
THFM fails to correctly account for the total number of magnetic subbands
within the narrow band i.e. its total Chern number, our method -- based on
projecting the light and heavy fermions onto the irreducible representations of
the magnetic translation group -- reproduces the correct total Chern number.
Analytical results presented here offer an intuitive understanding of the
nature of the (strongly interacting) Hofstadter bands.
