  In the standard model flavor violating decays of the top quark and of the
Higgs boson are highly suppressed. Further, the flavor violating decays of the
top and of the Higgs are also small in MSSM and not observable in current or in
near future experiment. In this work we show that much larger branching ratios
for these decays can be achieved in an extended MSSM model with an additional
vector like quark generation. Specifically we show that in the extended model
one can achieve branching ratios for $t\to h^0 c$ and $t\to h^0 u$ as large as
the current experimental upper limits given by the ATLAS and the CMS
Collaborations. We also analyze the flavor violating quark decay of the Higgs
boson, i.e., $h^0\to b\bar s + \bar b s$ and $h^0\to b\bar d + \bar b d$. Here
again one finds that the branching ratio for these decays can be as large as
$O(1)\%$. The analysis is done with inclusion of the CP phases in the Higgs
sector, and the effect of CP phases on the branching ratios is investigated.
Specifically the Higgs sector spectrum and mixings are computed involving
quarks and mirror quarks, squarks and mirror squarks in the loops consistent
with the Higgs boson mass constraint. The resulting effective Lagrangian with
inclusion of the vector like quark generation induce flavor violating decays at
the tree level. The test of the branching ratios predicted could come with
further data from LHC13 and such branching ratios could also be accessible at
future colliders such as the Higgs factories where the Higgs couplings to
fermions will be determined with greater precision.
