  The $\mathcal{\alpha}$ decay half-life of unknown nucleus $^{297}$Og is
predicted within two-potential approach, and $\mathcal{\alpha}$ preformation
probabilities of 64 odd-$A$ nuclei in the region of proton numbers $82<Z<126$
and neutron numbers $152<N<184$ from $^{251}$Cf to $^{295}$Og are extracted. In
addition, based on the latest experimental data, a new set of parameters for
$\mathcal{\alpha}$ preformation probabilities considering the shell effect and
proton-neutron interaction are obtained. The predicted $\mathcal{\alpha}$ decay
half-life of $^{297}$Og is 0.16 ms within a factor of 4.97 as well as the spin
and parity of ground states for nuclei $^{269}$Sg, $^{285}$Fl and $^{293}$Lv
are $3/2^+$, $3/2^+$ and $5/2^+$, respectively.
