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Core-shell microspheres have been applied in various research areas and, in particular, they are used in the generation of photonic nanojets with suitable design for photonic applications. The photonic nanojet is a narrow and focused high-intensity light beam emitting from the shadow-side of microspheres with tunable effective length, thus enabling its applications in biosensing technology. In this paper, we numerically studied the photonic nanojets brought about from biocompatible hydrogel core-shell microspheres with different optical properties. It was found that the presence of the shell layer can significantly affect the characteristics of the photonic nanojets, such as the focal distance, intensity, effective length, and focal size. Generally speaking, the larger the core-shell microspheres, the longer the focal distance, the stronger the intensity, the longer the effective length, and the larger the focal size of the generated photonic nanojets are. The numerical simulations of the photonic nanojets from the biocompatible core-shell microspheres on a Klarite substrate, which is a classical surface-enhancing Raman scattering substrate, showed that the Raman signals in the case of adding the core-shell microspheres in the system can be further enhanced 23 times in water and 108 times in air as compared in the case in which no core-shell microspheres are present. Our study of using tunable photonic nanojets produced from the biocompatible hydrogel core-shell microspheres shows potential in future biosensing applications. [ABSTRACT FROM AUTHOR]