We study the singular fractional‐order boundary‐value problem with a sign‐changing nonlinear term , , where n − 1 < α ≤ n, n ∈ ℕ and n ≥ 3 with 0 < μ1 < μ2 < ⋯<μn−2 < μn−1 and n − 3 < μn−1 < α − 2, aj ∈ ℝ, 0 < ξ1 < ξ2 < ⋯<ξp−2 < 1 satisfying , 𝒟α is the standard Riemann‐Liouville derivative, f : [0,1] × ℝn → ℝ is a sign‐changing continuous function and may be unbounded from below with respect to xi, and p : (0,1)→[0, ∞) is continuous. Some new results on the existence of nontrivial solutions for the above problem are obtained by computing the topological degree of a completely continuous field.