  We are concerned with gradient estimates for solutions to a class of singular
quasilinear parabolic equations with measure data, whose prototype is given by
the parabolic $p$-Laplace equation $u_t-\Delta_p u=\mu$ with $p\in (1,2)$. The
case when $p\in \big(2-\frac{1}{n+1},2\big)$ were studied in [15]. In this
paper, we extend the results in [15] to the open case when $p\in
\big(\frac{2n}{n+1},2-\frac{1}{n+1}\big]$ if $n\geq 2$ and $p\in(\frac{5}{4},
\frac{3}{2}]$ if $n=1$. More specifically, in a more singular range of $p$ as
above, we establish pointwise gradient estimates via linear parabolic Riesz
potential and gradient continuity results via certain assumptions on parabolic
Riesz potential.
