  The interplay of topological characteristics in real space and reciprocal
space can lead to the emergence of unconventional topological phases. In this
Letter, we implement a novel mechanism for generating higher-Chern flat bands
on the basis of twisted bilayer graphene (TBG) coupled to topological magnetic
structures in the form of the skyrmion lattice. In particular, we discover a
scenario for generating $|C|=2$ dispersionless electronic bands when the
skyrmion periodicity and the moir\'e periodicity are matched. Following the
Wilczek argument, the statistics of the charge-carrying excitations in this
case is \textit{bosonic}, characterized by electronic charge $Q =2e$, that is
\textit{even} in units of electron charge $e$. The required skyrmion coupling
strength triggering the topological phase transition is realistic, with its
threshold estimated as low as 4~meV. The Hofstadter butterfly spectrum of this
phase is different resulting in an unexpected quantum Hall conductance sequence
$\pm \frac{2 e^2}{h}, \ \pm \frac{4 e^2}{h}, ...$ for TBG with skyrmion order.
