  The Lie symmetry analysis for the study of a $1+n~$fourth-order
Schr\"{o}dinger equation inspired by the modification of the deformation
algebra in the presence of a minimum length is applied. Specifically, we
perform a detailed classification for the scalar field potential function where
non-trivial Lie symmetries exist and simplify the Schr\"{o}dinger equation.
Then, a qualitative analysis allows for the reduced ordinary differential
equation to be analyzed to understand the asymptotic dynamics.
