Summary: A \textit{signed graph} (or, in short, \textit{sigraph}) \(S=(S^u,\sigma)\) consists of an underlying graph \(S^u :=G=(V,E)\) and a function \(\sigma :E(S^u)\longrightarrow \{+,-\}\), called the signature of \(S\). A \textit{marking} of \(S\) is a function \(\mu :V(S)\longrightarrow \{+,-\}\). The \textit{canonical marking} of a signed graph \(S\), denoted \(\mu_\sigma\), is given as \[\mu_\sigma (v) := \prod_{vw \in E(S)} \sigma (vw).\] The \textit{line graph} of a graph \(G\), denoted \(L(G)\), is the graph in which edges of \(G\) are represented as vertices, two of these vertices are adjacent if the corresponding edges are adjacent in \(G\). There are three notions of a \textit{line signed graph} of a signed graph \(S=(S^u,\sigma)\) in the literature, viz., \(L(S)\), \(L_\times(S)\) and \(L_\bullet (S)\), all of which have \(L(S^u)\) as their underlying graph; only the rule to assign signs to the edges of \(L(S^u)\) differ. Every edge \(ee'\) in \(L(S)\) is negative whenever both the adjacent edges \(e\) and \(e'\) in \(S\) are negative, an edge \(ee'\) in \(L_\times (S)\) has the product \(\sigma (e) \sigma (e')\) as its sign and an edge \(ee'\) in \(L_\bullet(S)\) has \(mu_\sigma(v)\) as its sign, where \(v \in V(S)\) is a common vertex of edges \(e\) and \(e'\). The line-cut graph (or, in short, \textit{lict graph}) of a graph \(G=(V,E)\), denoted by \(L_c(G)\), is the graph with vertex set \(E(G)\cup C(G)\), where \(C(G)\) is the set of cut-vertices of \(G\), in which two vertices are adjacent if and only if they correspond to adjacent edges of \(G\) or one vertex corresponds to an edge \(e\) of \(G\) and the other vertex corresponds to a cut-vertex \(c\) of \(G\) such that \(e\) is incident with \(c\). In this paper, we introduce \textit{dot-lict signed graph} (or \textit{\(\bullet\)-lict signed graph} \(L_{\bullet_c}(S)\), which has \(L_c(S^u)\) as its underlying graph. Every edge \(uv\) in \(L_{\bullet_c}(S)\) has the sign \(\mu_\sigma (p)\), if \(u\), \(v \in E(S)\) and \(p\in V(S)\) is a common vertex of these edges, and it has the sign \(\mu_\sigma (v)\), if \(u \in E(S)\) and \(v \in C(S)\). we characterize signed graphs on \(K_p\), \(p\geq 2\), on cycle \(C_n\) and on \(K_{m,n}\) which are \(\bullet\)-lict signed graphs or \(\bullet\)-line signed graphs, characterize signed graphs \(S\) so that \(L_{\bullet_c}(S)\) and \(L_\bullet (S)\) are balanced. We also establish the characterization of signed graphs \(S\) for which \(S\sim L_{\bullet_c}(S)\), \(S\sim L_\bullet (S)\), \(\eta (S) \sim L_{\bullet_c}(S)\) and \(\eta (S) \sim L_\bullet (S)\), here \(\eta (S)\) is negation of \(S\) and \(\sim\) stands for switching equivalence.