In general, photonic nanojets (PNJs) occur only when the refractive index (Ri) difference between the microparticle and background media is less than 2. The minimum full width at half-maximum (FWHM) of the PNJ is ~130 nm (approximately one-third of the illumination wavelength λ = 400 nm) formed within the evanescent field region. This paper proposes and studies a method to overstep the Ri upper bound and generate ultra-narrow PNJs. Finite element method based numerical investigations and ray-optics theoretical analyses have realized ultra-narrow PNJs with FWHM as small as 114.7 nm (0.287 λ) obtained from an edge-cut, length-reduced and parabolic-profiled microparticle with Ri = 2.5 beyond evanescent decay length. Using simple strain or compression operations, sub-diffraction-limited PNJs can be flexibly tuned on the order of several wavelengths. Such ultra-narrow PNJs offer great prospects for optical nonlinearity enhancements of greater enhancing effect, optical nanoscopy of higher spatial resolution, optical microprobes of smaller measurement accuracy, nano/micro-sized sample detections of higher sensing sensitivity, nanoscale objects of more accurate control, advanced manufactures of smaller processing size, optical-disk storage of larger data capacity and all-optical switching of lower energy consumption.