  The Halperin $(m',m,n)$ fractional quantum Hall effects of two-component
quantum particles are studied in topological checkerboard lattice models. Here
for $m\neq m'$, we demonstrate the emergence of fractional quantum hall effects
with the associated $\mathbf{K}=\begin{pmatrix} m+2 & 1\\ 1 & m\\
\end{pmatrix}$ matrix (even $m=2$ for boson and odd $m=3$ for fermion) in the
presence of both strong intercomponent and intracomponent repulsions. Through
exact diagonalization and density-matrix renormalization group calculations, we
elucidate their topological fractionalizations, including (i) the
$\det|\mathbf{K}|=(m^2+2m-1)$-fold ground-state degeneracies and (ii)
fractionally quantized topological Chern number matrix
$\mathbf{C}=\mathbf{K}^{-1}$. Our flat band model provides a paradigmatic
example of a microscopic Hamiltonian featuring fractional quantum Hall effect
with partial spin-polarization.
