The contribution of spin fluctuations to the temperature and field dependence if the low-temperature spin susceptibility Χ(T) of exchange-enhanced paramagnets in finite magnetic fields is studied on the basis of the Fermi-liquid approach. It is shown that the proper evaluation of the terms in the free energy that are dependent on magnetic field H results in the appearance of the logarithmic temperature contribution to Χ(T). the existence of which was predicted earlier in Fermi-liquid approaches contribution to Χ(T). with the logarithrnic term, a new significant one which is proportional to T5/2/H1/2 has been found. The latter term can significantly change the usual interpretation of the experimenta data on the magnetic susceptibility in terms of the power series over the temperature and magnetic field. The reasons for these contributions not being found in previous considerations are discussed.