This study explored upper-limb and head kinematics during unimanual goal-directed movements in children born preterm (PT) and full-term (FT) aged 4-8 years. Further, functional lateralization was investigated through side-specific kinematics and hand preference observations. Altogether, 141 children were included, divided into three sub-groups based on gestation week at birth (GW). Children born FT (38-41 GW) and moderately PT (33-35 GW) showed faster, smoother, and shorter movement trajectories than children born very PT (V-PT < 33 GW). Only children born FT expressed evident side differences that were characterized by smoother movements with the preferred side. Regarding hand preference, the children born V-PT showed increased rates of non-right-handedness compared with the other groups. Regardless of hand preference, the children born V-PT showed less well organized movements compared with the other groups. These findings suggest that spatio-temporal movement organization and side specialization at pre-/early school-age are affected by a PT birth, and more frequently so for children born before 33 GWs, indicating long-lasting influences on neuromotor development and specialization.