We theoretically find that finite size Fulde-Ferrell (FF) superconductor (which is characterized by spatially nonuniform ground state Ψ ∼ exp(−iqF F r) and |Ψ|(r) = const in the bulk case, where Ψ is a superconducting order parameter) has paramagnetic Meissner, vortex and 'onion' ground states with |Ψ|(r) = const. These states are realized due to boundary effect when the lateral size of superconductor L ∼ 1/qF F . We argue, that predicted states could be observed in thin disk/square made of superconductor-ferromagnet-normal metal trilayer with L ≃ 150 − 600nm.