Current theories predict relativistic hadronic particle populations in clusters of galaxies in addition to the already observed relativistic leptons. In these scenarios hadronic interactions give rise to neutral pions which decay into γ rays that are potentially observable with the Large Area Telescope (LAT) on board the Fermi space telescope. We present a joint likelihood analysis searching for spatially extended γ-ray emission at the locations of 50 galaxy clusters in four years of Fermi-LAT data under the assumption of the universal cosmic-ray (CR) model proposed by Pinzke & Pfrommer. We find an excess at a significance of 2.7σ, which upon closer inspection, however, is correlated to individual excess emission toward three galaxy clusters: A400, A1367, and A3112. We discuss these cases in detail and conservatively attribute the emission to unmodeled background systems (for example, radio galaxies within the clusters).Through the combined analysis of 50 clusters, we exclude hadronic injection efficiencies in simple hadronic models above 21% and establish limits on the CR to thermal pressure ratio within the virial radius, R200, to be below 1.25%-1.4% depending on the morphological classification. In addition, we derive new limits on the γ-ray flux from individual clusters in our sample. © 2014. The American Astronomical Society. All rights reserved.