JWST/NIRSpec will be the first multi-object spectrograph (MOS) to fly in space and it will enable the simultaneous measurement of up to ∼ 200 spectra over the wavelength range ∼0.6 – 5.3 μm, allowing us to study the rest-frame optical properties of large samples of galaxies out to z∼ 9, and the rest-frame UV out to z > 10. To support the community in preparing NIRSpec MOS programs and getting ready to analyze the data, we present here a set of simulations closely mimicking the deep spectroscopic observations that will be performed as part of the JADES survey, a joint effort of the NIRCam and NIRSpec GTO teams. The simulations are made possible by the NIRSpec Instrument Performance Simulator software, a Fourier Optics wave propagation module coupled with a detailed model of the instruments optical geometry and radiometric response, and a detector simulator reproducing the noise properties and response of NIRSpec's two H2RG sensors. The targets for the simulations were selected from the JWST Extragalactic Mock Catalog, JAGUAR. The simulation data package delivered here include more than 60 count-rate images corresponding to the exposures break-down of the low and medium resolution part of one of the two NIRSpec deep-field spectroscopic programs of the JADES survey. The simulated data consists of three dither pointings, for 4 different instrument configurations (low and medium resolution over the entire NIRSpec wavelength range), plus the extracted, background subtracted, spectral traces for each of the 370 targets and corresponding 2D-rectified spectra and calibrated 1D spectra, as well as the mock astronomical data used as the simulation input.