In this study, we investigate observability of the neutral scalar ($H$) and pseudoscalar ($A$) Higgs bosons in the framework of the Type-I 2HDM at SM-like scenario at a linear collider operating at $sqrt s=$ 500 and 1000 GeV. The signal process chain $e^- e^+ rightarrow A H rightarrow ZHHrightarrow jj bbar{b}bbar{b}$ where $jj$ is a di-jet resulting from the $Z$ boson decay and $bbar{b}$ is a $b$ quark pair, is assumed and several benchmark scenarios with different mass hypotheses are studied. The assumed signal process is mainly motivated by the possible enhancements the decay modes $Arightarrow ZH$ and $Hrightarrow bbar{b}$ may receive in the Type-I. Event generation is performed for the assumed scenarios separately and the beamstrahlung effects are taken into account. The detector response is simulated based on the SiD detector at the ILC and the simulated events are analyzed to obtain candidate mass distributions of the Higgs bosons. According to the results, the top quark pair production process has the most contribution to the total background and is, however, well-controlled. Results indicate that, in all of the considered scenarios, both of the Higgs bosons $H$ and $A$ are observable with signals exceeding $5sigma$ with possibility of mass measurement. To be specific, at $sqrt s=500$ GeV, the region of parameter space with $m_H=150$ GeV and $200leq m_A leq 250$ GeV is observable at the integrated luminosity of 500 $fb^{-1}$. Also, at $sqrt s=1000$ GeV, the region with $150leq m_H leq 250$ GeV and $200leq m_A leq 330$ GeV with a mass splitting of 50-100 GeV between the $H$ and $A$ Higgs bosons is observable at the same integrated luminosity.
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