  Using the strong coupling diagram technique, low-temperature spectral
properties of the two-dimensional fermionic Hubbard model are con\-si\-de\-red
for strong and moderate Hubbard repulsions $U$. The electron hopping to the
nearest, second and third neighbors is taken into account with hopping
constants $t$, $t'=-0.3t$ and $t''=0.2t$, respectively. The nonzero values of
$t'$ and $t''$ lead to strong asymmetry in magnetic properties with respect to
the hole and electron doping -- for $U=8t$ strong antiferromagnetic
correlations are retained up to the electron concentration $\bar{n}\approx
1.25$, while they are destroyed completely at $\bar{n}\approx 0.87$. When the
temperature is decreased to $T\lesssim 0.1t$, in a wide range of electron
concentrations there appear narrow and intensive peaks at the Fermi level in
densities of states. For $U\lesssim 6t$ the peaks are seen even at
half-filling, while for larger $U$ they arise as the Fermi level leaves the
Mott gap. The peaks are connected with a narrow band emerging at low
temperatures. We identify states forming the band with spin-polaron excitations
-- bound states of correlated electrons and mobile spin excitations. Obtained
low-temperature spectral functions are used for interpreting the peak-dip-hump
structure observed in the photoemission of Nd$_{2-x}$Ce$_x$CuO$_4$. In the case
of hole doping, the calculated Fermi contour contains arcs near nodal points
with pseudogaps near antinodal points, while for electron doping the spectral
intensity is suppressed at hot spots, in agreement with experimental
observations in cuprate perovskites.
