An analysis of the local sources (LS) structure of the S-component of solar radio emission confirms the presence of a core component which is characterized by strong circular polarization and a steep growing spectrum at shorter centimeter wavelengths. These details coincide in position with the sunspots' umbra and their height above the photosphere does not generally exceed about 2000 km. Gyroresonance emission of thermal electrons of the corona is generally accepted as being responsible for this type of emission. The spectral and polarization observations of LS made with RATAN-600 using high resolution in the wavelength range 2.0-4.0 cm, allow us to measure the maximum magnetic fields of the corresponding sunspots at the height of the chromosphere-corona transition region (CCTR). This method is based on determining the short wavelength limit ofgyroresonance emission of the LS and relating it to the third harmonic ofgyrofrequency.An analysis of a large number of sunspots and their LS (core coml~onent) has shown a good correlation between radio magnetic fields near the CCTR and optical photospheric ones. The magnetic field in CCTR above a sunspot is found only 10 to 20% lower than in the photosphere. The resulting gradient of the field strength is not less than 0.25 G kin-~. This result seems to contradict the lower values of magnetic fields generally found above sunspots using the chromospheric H c~ line. Some possible ways of overcoming this difficulty are proposed.