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In this work, we introduce an extra singlet pseudoscalar into the Type-IIItwo Higgs doublet model (2HDM) which is supposed to solve a series of problemsin the modern particle-cosmology. With existence of a light pseudoscalar, the$h\rightarrow\mu\tau$ excess measured at CMS and as well as the $(g-2)_{\mu}$anomaly could be simultaneously explained within certain parameter spaces thatcan also tolerate the data on the flavor-violating processes$\tau\rightarrow\mu\gamma$ and Higgs decay gained at LHC. Within the sameparameter spaces, the DM relic abundance is well accounted. Moreover, therecently observed Galactic Center gamma ray excess(GCE) is proposed to realizethrough dark matter(DM) pair annihilations, and in this work, the scenario ofthe annihilation being mediated by the pseudoscalar is also addressed.

Type-III two Higgs doublet model plus a pseudoscalar confronted with $h\rightarrow\mu\tau$, muon $g-2$ and dark matter