  This paper aims to study the existence of asymmetric solutions for the
two-dimensional generalized surface quasi-geostrophic (gSQG) equations of
simply connected patches for $\alpha\in[1,2)$ in the whole plane, where
$\alpha=1$ corresponds to the surface quasi-geostrophic equations (SQG). More
precisely, we construct non-trivial simply connected co-rotating and traveling
patches with unequal vorticity magnitudes. The proof is carried out by means of
a combination of a desingularization argument with the implicit function
theorem on the linearization of contour dynamics equation. Our results extend
recent ones in the range $\alpha\in[0,1)$ by Hassainia-Hmidi (DCDS-A, 2021) and
Hassainia-Wheeler (SIAM J. Math. Anal., 2022) to more singular velocities,
filling an open gap in the range of $\alpha$.
