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Abstract In this paper, we study two Higgs doublet models with gauged $$U(1)_H$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>U</mml:mi> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mi>H</mml:mi> </mml:msub> </mml:mrow> </mml:math> symmetry instead of the usual softly broken $$Z_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Z</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> symmetry, motivated by the excesses around 96 GeV reported by the CMS collaboration in the searches for light resonances decaying to two photons and two $$\tau $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>τ</mml:mi> </mml:math> ’s. In this model, one Higgs doublet field is charged under the $$U(1)_H$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>U</mml:mi> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mi>H</mml:mi> </mml:msub> </mml:mrow> </mml:math> symmetry, thereby one can avoid tree-level flavor changing neutral currents. The extra $$U(1)_H$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>U</mml:mi> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mi>H</mml:mi> </mml:msub> </mml:mrow> </mml:math> gauge symmetry requires extra chiral fermions, in order to satisfy the anomaly-free conditions. We analyze the signals of the light resonances, taking into account the contribution of the extra fermions, and discuss the consistency with the experimental results in this model.