One-dimensional Ising systems in random fields (RFs) are studied taking into account the nearest-neighbour andnext-nearest-neighbour interactions. We investigate two distributions of RFs: binary and Gaussian distributions. Weconsider four cases of the exchange couplings: ferro-ferromagnetic (F-F), ferro-antiferromagnetic (F-AF), antiferro-ferromagnetic (AF-F) and antiferro-antiferromagnetic (AF-AF). The energy minima of chains of no more than 30 spinswith periodic boundary conditions are analysed exactly. We found that the average number of energy minima growsexponentially with the number of spins in both cases of RFs.The energy distributions across the corresponding energyminima are shown. The effects of RFs on both the average and density of metastable states are explained. For a weakRF, the energy distributions display a multipartitioned structure. We also discuss the frustration effect due to RFsand exchange fields. Finally, the distributions of magnetization are calculated. The absolute value of magnetizationaveraged over all metastable states decreases logarithmically with the number of spins.