Structures in the ground state and thermodynamics related to melting of spherical Yukawa and Coulomb clusters confined in external fields of less than 103 particles are discussed on the basis of molecular dynamics and Monte Carlo simulations and theoretical methods. At low temperatures, particles form concentric shell structures which are expressed by simple formulas and insensitive to the strength of screening. Structures are reproduced by the shell model when the intrashell cohesive energy is properly taken into account. The specific heat of clusters of relatively small sizes 100 ≤ Nd ≤ 400 has two peaks as a function of temperature. By analyses of diffusions, it is shown that the peaks at lower and higher temparatures corresponds to the loss of ordering in the azimuthal and radial (and therefore total) ordering, respectively. Magnitudes of fluctuations in the outermost shell are consistent with the conventional Lindemann criterion.