  The roles of the fine-structure intramanifold resonances to the Zeeman shifts
caused by the blackbody radiation (BBRz shifts) in the optical clock
transitions are analyzed. The clock frequency measurement in the $^1S_0-^3P_0$
clock transition of the singly charged aluminium ion (Al$^+$) has already been
reached the $10^{-19}$ level at which the BBRz effect can be significant in
determining the uncertainty. In view of this, we probe first the BBRz shift in
this transition rigorously and demonstrate the importance of the contributions
from the intramanifold resonances explicitly. To carry out the analysis, we
determine the dynamic magnetic dipole (M1) polarizabilities of the clock states
over a wide range of angular frequencies by employing two variants of
relativistic many-body methods. This showed the BBRz shift is highly suppressed
due to blue-detuning of the BBR spectrum to the $^3P_0-^3P_1$ fine-structure
intramanifold resonance in Al$^+$ and it fails to follow the usually assumed
static M1 polarizability limit in the estimation of the BBRz shift. The
resonance also leads to a reversal behavior of the temperature dependence and a
cancellation in the shift. After learning this behavior, we extended our
analyses to other optical clocks and found that these shifts are of the order
of micro-hertz leading to fractional shifts in the clock transitions at the
$10^{-20}$ level or below.
