  We study the interplay between superconductivity and antiferromagnetic spin
fluctuations in electron-doped cobaltate Na$_{x}$CoO$_{2}\cdot y$H$_{2}$O based
on the kinetic energy driven superconductivity mechanism. We show that the
superconducting state is governed by both charge carrier pairing and
quasiparticle coherent, and displays a common dome-shaped phase diagram in
agreement with experimental results. By calculating the dynamical spin
structure factor, we theoretically find that the magnetic excitation shows a
commensurate resonance peak, which locates at antiferromagnetic wave vector $Q
(\frac{2\pi}{3},\frac{2\pi}{\sqrt{3}})$ for a broad range of low energies, then
evolves outward into six incommensurate magnetic scattering peaks with
increasing energy. Such commensurate-incommensurate spin resonance excitation
should be measured by the inelastic neutron scattering technique (INS). Our
present results strongly suggest that magnetic resonance can indeed be one of
the fundamental features in doped Mott insulators.
