An Electron Beam Probe (EBP) is preferable to provide a non-interceptive measurement of the transverse distribution of a dense bunched ion beam. During EBP operation, it was observed that the electron beam spot subjects to expansion when scanned across the ion beam due to the strong space charge field of the ion bunch, leading to significant degradation of spatial resolution. To mitigate this effect, a small electron beam spot is beneficial as demonstrated in previous research. This paper presents design details of a low-emittance, small-spot, and long-work-distance electron gun. Geometry optimization of the gun and focus lens is conducted using a multiobjective genetic algorithm (MOGA) interfaced with space charge simulation codes to maintain normalized thermal emittance within an acceptable increase and achieve a small spot at a long work distance. The emittance is measured using a slit-screen technique, resulting in a norm. rms emittance of 0.046(+-0.005) um*rad under low beam current conditions (50 nA). In high-resolution mode, a beam spot size of 0.6 mm (rms) is achieved at a work distance of 1.2 m with the combination of Einzel lens and solenoid. The gun has been successfully operated as part of EBP experiments for accurate and high-resolution measurement of ion beam width, demonstrating excellent agreement with wire scanner measurements with relative deviation not exceeding 1%.