We study low energy implications of F-theory GUT models based on $SU(5)$ extended by a $U(1)$ symmetry which couples non-universally to the three families of quarks and leptons. This gauge group arises naturally from the maximal exceptional gauge symmetry of an elliptically fibred internal space, at a single point of enhancement, $E_8supset SU(5)times SU(5)supset SU(5)times U(1)^4$. Rank-one fermion mass textures and a tree-level top quark coupling are guaranteed by imposing a $Z_2$ monodromy group which identifies two abelian factors of the above breaking sequence. The $U(1)$ factor of the gauge symmetry is an anomaly free linear combination of the three remaining abelian symmetries left over by $Z_2$. Several classes of models are obtained, distinguished with respect to the $U(1)$ charges of the representations, and possible extra zero modes coming in vector-like representations. The predictions of these models are investigated and are compared with the LHC results and other related experiments. Particular cases interpreting the B-meson anomalies observed in LHCb and BaBar experiments are also discussed.
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