We consider quasilinear parabolic equations with measurable coefficients when the right-hand side is a signed Radon measure finite total mass, having $p$-Laplace type: $$u_t - \textrm{div} \, \mathbf{a}(Du,x,t) = \mu \quad \textrm{in} \ \Omega \times (0,T) \subset \mathbb{R}^n \mathbb{R}.$$ In singular range $\frac{2n}{n+1} <p \le 2-\frac{1}{n+1}$, we establish regularity estimates for spatial ...