The aim of this paper is to establish new pointwise regularity results for solutions degenerate second-order partial differential equations with a Kolmogorov-type operator the form $$\begin{aligned} {\mathscr {L}}:=\sum _{i,j=1}^m \partial ^2_{x_i x_j } +\sum _{i,j=1}^N b_{ij}x_j\partial _{x_i}-\partial _t, \end{aligned}$$ where $$(x,t) \in {{\mathbb {R}}}^{N+1}$$ , $$1 \le m N$$ and matrix $$B...