  The evolution of the temperature dependence of pseudogap $\Delta$*(T) in
optimally doped (OD) YBa$_2$Cu$_3$O$_{7-\delta}$ (YBCO) films with $T_{c}$ =
88.7 K under the influence of a magnetic field $B$ up to 8 T has been studied
in detail. It has been established that the shape of $\Delta$*(T) for various
$B$ over the entire range from the pseudogap opening temperature $T$* to
$T_{01}$, below which superconducting fluctuations occur, has a wide maximum at
the BEC-BCS crossover temperature $T_{pair}$, which is typical for OD films and
untwinned YBCO single crystals. $T$* was shown to be independent on $B$,
whereas $T_{pair}$ shifts to the low temperature region along with increase of
$B$, while the maximum value of $\Delta$*($T_{pair}$) remains practically
constant regardless of $B$. It was revealed that as the field increases, the
low-temperature maximum near the 3D-2D transition temperature $T_{0}$ is
blurred and disappears at $B$ > 5 T. Moreover, above the Ginzburg temperature
$T_{G}$, which limits superconducting fluctuations from below, at $B$ > 0.5 T,
a minimum appears on $\Delta$*(T) at $T_{min}$, which becomes very pronounced
with a further increase in the field. As a result, the overall value of
$\Delta$*(T) decreases noticeably most likely due to pair-breaking affect of a
magnetic field. A comparison of $\Delta$*(T) near $T_{c}$ with the Peters-Bauer
theory shows that the density of fluctuating Cooper pairs actually decreases
from <<n$_{\uparrow}$n$_{\downarrow}$>> $\approx$ 0.31 at $B$ = 0 to
<<n$_{\uparrow}$n$_{\downarrow}$>> $\approx$ 0.28 in the field 8 T. The
observed behavior of $\Delta$*(T) around $T_{min}$ is assumed to be due to the
influence of a two-dimensional vortex lattice created by the magnetic field,
which prevents the formation of fluctuating Cooper pairs near $T_{c}$.
