We consider the following higher-order Schrödinger equation involving supercritical growth and competing potentials: * \(\begin{aligned} {\left\{ \begin{array}{ll} (-\Delta )^m u + V(y) u=Q(y)u^{m^*-1+\varepsilon }, \;u>0, & \hbox { in } \mathbb {R}^{N}, \\ u \in \mathcal {D}^{m,2}(\mathbb {R}^{N}), \end{array}\right. } \end{aligned}\) where \(m^*=\frac{2N}{N-2m},\; N\ge 4m+1\) , \(m \ge 2\) is an integer, \((y',y'') \in \mathbb {R}^{2} \times \mathbb {R}^{N-2}\) , \(V(y) = V(|y'|,y'')\) and \(Q(y) = Q(|y'|,y'') \not \equiv 0\) are two bounded nonnegative functions. By using the finite-dimensional reduction argument and local Pohozaev-type identities, under some suitable assumptions on the potentials V and Q, we prove that for any small \(\varepsilon > 0\) , the problem \((*)\) has a large number of bubble solutions whose functional energy is in the order \(\varepsilon ^{-\frac{N-4m}{(N-2m)^2}}.\)
