Summary: We obtain scalar hairy black holes from Einstein-Maxwell-conformally coupled scalar (EMCS) theory with the scalar coupling parameter \(\alpha\) to the Maxwell term. In case of \(\alpha = 0\), the \(\alpha = 0\) EMCS theory provides constant (charged) scalar hairy black hole and charged BBMB (Bocharova-Bronnikov-Melnikov-Bekenstein) black hole where the former is stable against full perturbations, while the latter remains unstable because it belongs to an extremal black hole. It is noted that for \(\alpha \neq 0\), the unstable Reissner-Nordström black holes without scalar hair imply infinite branches of \(n = 0(\alpha \geq 8.019), 1(\alpha \geq 40.84), 2(\alpha \geq 99.89), \cdots\) scalarized charged black holes. In addition, for \(\alpha > 0\), we develop a single branch of scalarized charged black hole solutions inspired by the constant scalar hairy black hole. Finally, we obtain the numerical charged BBMB black hole solution from the \(\alpha = 0\) EMCS theory.