Summary: In this paper, we explore some emerging properties of the stellar objects in the frame of the \(f(R, \phi)\) gravity by employing the well-known Karmarkar condition, where \(R\) and \(\phi\) represent the Ricci scalar and scalar potential, respectively. We demonstrate the embedded class-I technique by using the static spherically symmetric line element along with anisotropic fluid matter distribution. Furthermore, to achieve our goal, we take a specific expression of metric potential \(g_{rr}\), already presented in the literature, and proceed by using the Karmarkar condition to obtain the second metric potential. To get the value of unknown parameters of the compact structures, we compare the Krori-Barua spacetime with spherically symmetric spacetime. Moreover, we examine the physical attributes of compact objects by presuming three viable \(f(R, \phi)\) models. We analyze the graphical behavior of density and pressure, the Tolman-Oppenheimer-Volkoff equation, energy conditions, mass function, surface redshift, and adiabatic index. It is recognized that all the obtained results deliver emphatic evidence for the stability of our considered realistic stars.