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We explore the low energy implications of an F-theory inspired $E_6$ modelwhose breaking yields, in addition to the MSSM gauge symmetry, a $Z'$ gaugeboson associated with a $U(1)$ symmetry broken at the TeV scale. The zero modespectrum of the effective low energy theory is derived from the decompositionof the $27$ and $\overline{27}$ representations of $E_6$ and we parametrisetheir multiplicities in terms of a minimum number of flux parameters. Weperform a two-loop renormalisation group analysis of the gauge and Yukawacouplings of the effective theory model and estimate lower bounds on the newvectorlike particles predicted in the model. We compute the third generationYukawa couplings in an F-theory context assuming an $E_8$ point of enhancementand express our results in terms of the local flux densities associated withthe gauge symmetry breaking. We find that their values are compatible with theones computed by the renormalisation group equations, and we identify points inthe parameter space of the flux densities where the $t-b-\tau$ Yukawa couplingsunify.

Vectorlike Particles, $Z'$ and Yukawa Unification in F-theory inspired $E_6$