Probing flavor parameters in the scalar sector and new bounds for the fermion sector

In this paper we study the Flavor-Changing mediated by Higgs boson within Two-Higgs Doublet Model-III context. We explore the parameter space and, considering recent results, find new limits for the model parameters. We also obtain the total Higgs decay width and the branching ratios for different channels taking limits for the $t\to cV$ and $b\to s\gamma$ processes. Considering different constraints, we estimate the branching ratio for the $h\to t_{}^{\ast }c$ in the model as well as the bounds for the $b\to s\gamma$, $h \to \mu\tau$and$h\to \gamma Z.$Consideringthequarktopdecaysto$W\bar{b},$weobtained$Br(h \to Wc\bar{b})\sim10^{-3}$.