The mean-field electronic specific heat of a superconductor in the presence of a magnetic field is calculated. We consider an energy spectrum presenting saddle points in the band structure. They correspond to Van Hove singularities in the density of states. We use a three-dimensional band structure by introducing a coupling energy between the CuO2 planes. Both s-wave and d-wave energy-gap-parameter cases are investigated. It is noticed that the specific-heat jump should increase or decrease with the field, respectively. It is found that the d-wave model seems to be qualitatively and quantitatively more realistic. The influence of a magnetic field on the jump of the electronic specific heat of various high-T-c superconductors such as YBa2Cu3O7-x, HgBa2Ca2Cu3O8, and Tl2Ba2CuO6+delta near T-c is compared to mean-field results. Fluctuations are extracted and analyzed. It is pointed out that the mean-field background should be extracted before analyzing the fluctuations. Critical fluctuation regimes, Gaussian, lowest Landau level, and XY regimes as well as the effective dimensionality of the systems are obtained. The field regimes are given on the T-c line.