AbstractIn this paper, we study the singularly perturbed fractional Choquard equationε2s(−Δ)su+V(x)u=εμ−3(∫R3|u(y)|2μ,s∗+F(u(y))|x−y|μdy)(|u|2μ,s∗−2u+12μ,s∗f(u))inR3,$$\begin{equation*}\varepsilon^{2s}(-{\it\Delta})^su+V(x)u=\varepsilon^{\mu-3}(\int\limits_{\mathbb{R}^3}\frac{|u(y)|^{2^*_{\mu,s}}+F(u(y))}{|x-y|^\mu}dy)(|u|^{2^*_{\mu,s}-2}u+\frac{1}{2^*_{\mu,s}}f(u)) \, \text{in}\, \mathbb{R}^3, \end{equation*}$$whereε> 0 is a small parameter, (−△)sdenotes the fractional Laplacian of orders ∈(0, 1), 0 <μ< 3,2μ,s⋆=6−μ3−2s$2_{\mu ,s}^{\star }=\frac{6-\mu }{3-2s}$is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality and fractional Laplace operator.Fis the primitive offwhich is a continuous subcritical term. Under a local condition imposed on the potentialV, we investigate the relation between the number of positive solutions and the topology of the set where the potential attains its minimum values. In the proofs we apply variational methods, penalization techniques and Ljusternik-Schnirelmann theory.