Rota-Baxter family $\mathrm{\Omega }$-associative conformal algebras and their cohomology theory

In this paper, we first propose the concept of Rota-Baxter family $\mathrm{\Omega }$-associative conformal algebras, then we study the cohomology theory of Rota-Baxter family $\mathrm{\Omega }$-associative conformal algebras of any weight and justify it by interpreting the lower degree cohomology groups as formal deformations.