[en] The electronic structures and magnetic properties of a new series of quaternary Heusler alloys CoFeScZ (Z=P, As, Sb) are investigated through first-principle calculations. CoFeScP is found to have half-metallic ferromagnetism with a large half-metallic gap of 0.60 eV. The results show that both CoFeScAs and CoFeScSb are nearly half-metal under the equilibrium lattice constants. The change of the properties of CoFeScAs and CoFeScSb with pressure is investigated. - Highlights: • Investigate a new series of quaternary Heusler alloys CoFeScZ (Z=P, As, Sb). • The band gap of the half-metal CoFeScP is very large. • Study the magnetic properties and electronic structure of CoFeScP under the equilibrium lattice constant. • Investigate the influence of pressure on the magnetic properties and electronic structure of CoFeScAs and CoFeScSb