Three-photon resonance enhancement of third-harmonic generation and multiphoton ionization have been studied in xenon under excitation by the Bessel and the focused annular laser beams. It has been shown that the transformation of a Gaussian beam into a Bessel or an annular one leads to significant changes of third-harmonic excitation profiles and ionization spectra. These changes result from a principal difference of the beams, where either collinear (Gaussian beams) or noncollinear (Bessel and focused annular beams) excitation geometries are realized. It has been shown that the noncollinear ring-type phase matching shifts the maximum of the generated third harmonic to the longer wavelength toward the atomic resonance. Numerical calculations of third-harmonic excitation spectra have been carried out and compared with experimental results. The efficiency of frequency tripling in collinear and noncollinear excitation geometries have been compared. Cancellation of the three-photon
6s resonance and the influence of harmonic photons on the excitation of the four-photon
4f resonance in the Bessel beams are discussed.