  We investigate the chiral-even twist-3 generalized parton distributions
(GPDs) of valence quarks in the proton at nonzero skewness $\xi$, using a
spectator model with scalar and axial-vector diquarks. We consider the
exponential form factor for the nucleon-quark-diquark vertex and the
axial-vector diquark with light-cone transverse polarization. We analyze the
dependence of GPDs on the longitudinal momentum fraction $x$ at different
$\xi$, and on the square of the transverse momentum transfer $\Delta^2_T$ at
different $x$. Our numerical results reveal distinct discontinuities in all
twist-3 GPDs except $G_1$ and $\tilde{G}_1$. By taking the forward limit, we
obtain the twist-3 parton distribution function $g_T$, which encodes the
transverse spin distribution of quarks. We also compare the kinetic orbital
angular momentum and the spin-orbit correlations of quarks defined by the
twist-2 and twist-3 GPDs, respectively.
