In this talk I will describe the normal stable surfaces with \(K^2=2p_g-3\) whose only non canonical singularity is a cyclic quotient singularity of type \(\frac{1}{4k}(1,2k-1)\) and the corresponding locus \(\mathfrak D\) inside the KSBA moduli space of stable surfaces. The main result is the following: for \(p_g\ge 15\), (1) a general point of any irreducible component of \(\mathfrak D\) corresponds to a surface with a singularity of type \(\frac 14(1,1) \), (2) the closure of \({\mathfrak D}\) is a divisor contained in the closure of the Gieseker moduli space of canonical models of surfaces with \(K^2=2p_g-3\) and intersects all the components of such closure, and (3) the KSBA moduli space is smooth at a general point of \(\mathfrak D\). Moreover \(\mathfrak D\) has 1 or 2 irreducible components, depending on the residue class of \(p_g\) modulo 4. This is joint work with Rita Pardini.