The closed-form analytical expressions for the off-shell solutions for Hulthén-distorted Yamaguchi potential are derived to deal with the charged hadron systems. To construct these solutions, the particular integrals of the non-homogeneous Schrödinger equations are utilised in conjunction with the interacting Green’s functions. The Jost functions thus obtained, both on- and off-shell, are exploited to find the half-off-shell T -matrix. The off shell Jost function exists but off-shell Jost solution for the said potential has not yet been discussed in the literature. The merits of the T -matrix are examined through some model calculations. Exploiting the expressions for on and half-shell transition matrices, the s-wave elastic and inelastic scattering cross-sections are also estimated. Our results for the proton–proton and proton–oxygen systems are in close agreement with other calculations.