We report our combined experimental and theoretical study of magnetoelectric properties of an antiferromagnet $\mathrm{Sr}(\mathrm{TiO}){\mathrm{Cu}}_{4}{({\mathrm{PO}}_{4})}_{4}$ in comparison with the isostructurals $\mathrm{Ba}(\mathrm{TiO}){\mathrm{Cu}}_{4}{({\mathrm{PO}}_{4})}_{4}$ and $\mathrm{Pb}(\mathrm{TiO}){\mathrm{Cu}}_{4}{({\mathrm{PO}}_{4})}_{4}$. The family of compounds commonly possesses a low-symmetric magnetic unit called the square cupola, which is a source of magnetoelectri...