  As generalizations of Rota--Baxter groups, Rota--Baxter Clifford semigroups
have been introduced by Catino, Mazzotta and Stefanelli in 2023. Based on their
pioneering results, we continue to study Rota--Baxter Clifford semigroups and
their generalizations in the present paper. Inspired by the corresponding
results in Rota--Baxter groups, we firstly obtain some properties and
construction methods for Rota--Baxter Clifford semigroups, and then study the
substructures and quotient structures of these semigroups. On the other hand,
we introduce the notion of relative Rota--Baxter Clifford semigroups and
explore the relationship between these semigroups and dual weak left braces,
which are known to give set-theoretical solutions of the Yang--Baxter equation.
More specifically, we show that every relative Rota--Baxter Clifford semigroup
gives rise to a dual weak left brace, and conversely, every dual weak left
brace can be obtained from a bijective strong relative Rota--Baxter Clifford
semigroup. Furthermore, it turns out that there is an equivalence between the
two categories of bijective strong Rota--Baxter Clifford semigroups and dual
weak left braces. The substructures and quotient structures of Rota--Baxter
Clifford semigroups are also considered.
