Recently, ferroelectric liquid crystals (FLCs) doped with nanoparticles have attracted a wide interest not only from a scientific but also from a practical point of view and there is continuously growing interest in the effects caused by doping the ferroelectric nanoparticles. Furthermore, the presence of external fields exhibits a very interesting transition, reported by recent experiments. In this work, we investigate the response of a surface stabilized ferroelectric liquid crystal (SSFLC) doped with ferroelectric nanoparticles to an applied electric field. We assume that the smectic layers consist of uniform planes with a fixed orientation and the system is free from dislocation of constant layer thickness due to nanoparticles. We obtain the threshold field of orientational transition and the maximum deviation of the polarization vectors for a pure and a doped SSFLC medium. Then, we discuss the Fredericks transtion of the system and formation of inhomogeneous texture. It is found that the ferroelectric nanoparticles have significant influences in ordering behavior of a SSFLC medium and the threshold fields are critically changed by doping nanoparticles in the SSFLC, which is fundamental to operation of many liquid crystal devices.