The paper presents high-resolution experimental study and a direct potential construction of a shelflike state E(4)(1)Σ(+) of the KCs molecule converging to K(4(2)S) + Cs(5(2)D) atomic limit; such data are of interest for selecting optical paths for producing and monitoring cold polar diatomics. The collisionally enhanced laser induced fluorescence (LIF) spectra corresponding to both spin-allowed E(4)(1)Σ(+) → X(1)(1)Σ(+) and spin-forbidden E(4)(1)Σ(+) → a(1)(3)Σ(+) transitions of KCs were recorded in visible region by Fourier transform spectrometer with resolution of 0.03 cm(-1). Overall about 1650 rovibronic term values of the E(4)(1)Σ(+) state of (39)K(133)Cs and (41)K(133)Cs isotopologues nonuniformly covering the energy range [16987, 18445] cm(-1) above the minimum of the ground X-state were determined with the uncertainty of 0.01 cm(-1). Experimental data field is limited by vibrational levels v' ∈ [2, 74] with rotational quantum numbers J' ∈ [1, 188]. The closed analytical form for potential energy curve (PEC) based on Chebyshev polynomial expansion (CPE) was implemented to a direct potential fit (DPF) of the experimental term values of the most abundant (39)K(133)Cs isotopologue. Besides analyticity, regularity, correct long-range behavior, and nice convergence properties, the CPE form demonstrated optimal balance on flexibility and constraint for the DPF of a shelflike state aggravated by a limited data set. The mass-invariant properties of the CPE PEC were tested by the prediction of rovibronic term values of the (41)K(133)Cs isotopomer which coincided with their experimental counterparts with standard deviation of 0.0048 cm(-1). The CPE modeling is compared with the highly flexible pointwise inverted perturbation approach model, as well as with conventional Dunham analysis of restricted data set v' ≤ 50. Reliability of the empirical PEC is additionally confirmed by good agreement between the calculated and experimental relative intensity distributions in the long E(v') → X(v") LIF progressions.