Nuclotron based Ion Collider fAcility (NICA) is a flagship project of the Joint Institute for Nuclear Research which is expected to be operational by 2021. Main tasks of “NICA Facility” are study of hot and dense baryonic matter, investigation the polarisation phenomena and the nucleon spin structure. The material presented here based on the Letter of Intent (LoI) dedicated to nucleon spin structure studies at NICA. Measurements of asymmetries in the lepton pair (Drell-Yan) production in collisions of non-polarised, longitudinally and transversely polarised proton and deuteron beams to be performed using the specialized Spin Physics Detector (SPD). These measurements can provide an access to all leading twist collinear and Transverse Momentum Dependent Parton Distribution Functions (TMD PDFs) in nucleons. The measurements of asymmetries in production of J/ψ and direct photons, which supply complimentary information on the nucleon structure, will be performed simultaneously. The set of these measurements permits to tests the quark-parton model of nucleons at the QCD twist-2 level with minimal systematic errors.