The goals of this work are to design and develop a technology for fabrication and study of multifunctional properties of core/shell nanoparticles (NPs) as magnetic/luminescent markers. The new hybrid core/shell Fe₃O₄/Gd₂O₃:1% Er³⁺, 18% Yb³⁺, 2.5% Mg²⁺, x% Nd³⁺ NPs doped with different concentrations of neodymium ions, where x = 0%, 0.5%, 0.75%, 1%, 2%, 4%, were synthesized by the co-precipitation method. The NPs were characterised using XRD, TEM, SEM, EDX, confocal microscopy and photoluminescence. Fe₃O₄ (core) consists of several 13 nm NPs. The core/shell NPs have sizes from 220 nm to 641 nm. In this latter case, the shell thicknesses were 72, 80, and 121 nm. The upconversion efficiency properties and magnetic properties of the hybrid NPs were investigated. In the core/shell NPs, the addition of Nd³⁺ quenches the luminescence. The magnetic response of core/shell samples is rather paramagnetic and does not differ significantly from that registered for the shell material alone. For Gd₂O₃:1% Er³⁺, 18% Yb³⁺ and Fe₃O₄/Gd₂O₃:1% Er³⁺, 18% Yb³⁺, 2.5% Mg²⁺, 0.5% Nd³⁺, at 300 K, the values of the magnetization registered at ~ 40 kOe are similar and equal to ~ 5.3 emu·g⁻¹. The survivability of the HeLa tumor cells with the presence of the core/shell NPs was investigated for 24 h. The NPs are non-toxic up to a concentration of 1000 µg·ml⁻¹ and penetrate cells in the process of endocytosis which has been confirmed by confocal microscope studies.