In the present paper, we investigate the existence, multiplicity and concentration of normalized solutions to the following fractional Schrödinger equation with potential \(\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^s u+V(\varepsilon x)u+\lambda u=f(u), \ x \ \in \mathbb {R}^N,\\ \int _{\mathbb {R}^N}|u|^2dx=a^2,\\ \end{array} \right. \end{aligned}\) where \(0<s<1\) , \(N\ge 2\) , \(a, \ \varepsilon >0\) , \(V \in C(\mathbb {R}^N, \mathbb {R})\) is a local potential, \(\lambda \) is an unknown parameter that will appear as a Lagrange multiplier, f is a mass subcritical and Sobolev subcritical nonlinearity. Under fairly general assumptions about f and a local condition about V, with the aid of the penalization method, minimization techniques and Ljusternik-Schnirelmann category theory, we study the relation between the numbers of normalized solutions and the topology of the set where the potential V attains its minimum value.
