We investigate many-body effects on a mixture of interacting bosons and fermions loaded in an optical lattice using a generalized dynamical mean-field theory combined with the numerical renormalization group. We show that strong correlation effects emerge in the presence of bosonic superfluidity, leading to a renormalized peak structure near the Fermi level in the density of states for fermions. Remarkably, this kind of strong renormalization appears not only in the metallic phase but also in the insulating phases of fermions such as in the empty-and filled-band limit. A systematic analysis of the relation between the quasiparticle weight and the strength of superfluidity reveals that the renormalization effect is indeed caused by the boson degrees of freedom. It is found that such renormalization is also relevant to a supersolid phase consisting of a density-wave ordering of fermions accompanied by bosonic superfluidity. This sheds light on the origin of the peak structure in the supersolid phase.