We report the structure of a modulated phase in the ferroelectric nematic material RM734 under cationic-polymer-coated planar confinement. This phase emerges continuously from the nematic phase upon cooling and transforms into the ferroelectric nematic phase via a first-order transition. Compelling optical evidence, including thickness-dependent periodicity, a sinusoidal variation of the orientation angle, and periodic variations in phase retardance and image intensity, demonstrates that this modulated phase is the theoretically predicted double splay nematic phase. In this phase, splay deformations alternate along two orthogonal directions oriented at 45° to the substrate surfaces, resulting in a maximum modulation wavelength twice the cell thickness. Our experiments with various ionic coatings reveal that only cationic polymer coatings effectively promote this phase configuration, highlighting the crucial role of electrical screening. These findings further provide insights into its distinctive topological defects within confined geometries.