  Three-dimensional topological insulators (3D-TIs) possess a specific
topological order of electronic bands, resulting in gapless surface states via
bulk-edge correspondence. Exotic phenomena have been realized in ferromagnetic
TIs, such as the quantum anomalous Hall (QAH) effect with a chiral edge
conduction and a quantized value of the Hall resistance ${R_{yx}}$. Here, we
report on the emergence of distinct topological phases in paramagnetic Fe-doped
(Bi,Sb)${_2}$Se${_3}$ heterostructures with varying structure architecture,
doping, and magnetic and electric fields. Starting from a 3D-TI, a
two-dimensional insulator appears at layer thicknesses below a critical value,
which turns into an Anderson insulator for Fe concentrations sufficiently large
to produce localization by magnetic disorder. With applying a magnetic field, a
topological transition from the Anderson insulator to the QAH state occurs,
which is driven by the formation of an exchange gap owing to a giant Zeeman
splitting and reduced magnetic disorder. Topological phase diagram of
(Bi,Sb)${_2}$Se${_3}$ allows exploration of intricate interplay of topological
protection, magnetic disorder, and exchange splitting.
