This paper investigates the existence of normalized solutions with prescribed L2-norm to the nonlinear Choquard equation \(\left\{{\matrix{{- \Delta u + V(x)u + \lambda u = \mu ({{J_\alpha} * {{| u |}^p}}){{| u |}^{p - 2}}u} \hfill & {\text{in}\,{\mathbb{R}^N},} \hfill \cr {\int_{{\mathbb{R}^N}} {{u^2}dx = a,}}\hfill}}\right.\) here N ≥ 3, μ > 0, V(x) ≤ 0, and λ is an unknown Lagrange multiplier. Initially, we establish the existence of the minimizer of the L2-constraint minimization problem when \(2 < p < {{N + \alpha + 2} \over N}\) , with α ∈ (N − 2, N). Next, we derive a mountain pass solution under an explicit smallness assumption on V when \({{N + \alpha + 2} \over N}<p<{{N + \alpha} \over N-2}\) with α ∈ (0, N). Lastly, we identify two solutions in the case of a smaller mass, which is dependent on V, and falls within the range \({{N + \alpha + 2} \over N}<p<{{N + \alpha} \over N-2}\) , with α ∈ (0, N). Specifically, the first solution represents a local minimizer, and we analyze the compactness of the minimizing sequence. The second solution, at a positive energy level, is obtained through mountain pass arguments.
