In this article, we discuss interpolating sesqui-harmonic slant curves in generalized Sasakian space form and find the necessary and sufficient conditions for slant curves to be interpolating sesqui-harmonic. Next, we study sesqui minimal slant curves in generalized Sasakian space form. In particular we give an example of interpolating sesqui-harmonic slant curve in Sasakian space form. Our paper generalizes the results of the papers [8, 16, 20]