Using Coulomb-Yukawa like correlated interaction potentials of integer and noninteger indices the series expansion formulae in terms of multicenter overlap integrals of three complete orthonormal sets of ${psi}^{alpha}$?exponential type orbitals and linear combination coefficients of molecular orbitals are established for the potential of electrostatic field produced by the charges of molecule, where $alpha$ = 1, 0, ?1, ?2,${cdots}$. The formulae obtained can be useful for the study of interaction between atomic--molecular systems containing any number of closed and open shells when the ${psi}^{alpha}$?exponential type basis functions and Coulomb-Yukawa like correlated interaction potentials are used in the Hartree-Fock-Roothaan and explicitly correlated approximations. The final results are valid for the arbitrary values of parameters of correlated interaction potentials and orbitals. As an example of application, the calculations have been performed for the potential energy of interaction between electron and molecule $H_2O$ using combined Hartree-Fock-Roothaan equations suggested by the author.