  Utilizing a tritter with variable parameter $T$ and induced by
vacuum-one-photon superpositions $\left\vert 0\right\rangle +\alpha \left\vert
1\right\rangle $ with $\alpha =\left\vert \alpha \right\vert e^{i\phi }$, we
generate a class of three-qubit pure states. These states take the form of
$\left\vert \psi \right\rangle _{123}=c_{0}\left\vert 000\right\rangle
+c_{1}\left\vert 100\right\rangle +c_{2}\left\vert 010\right\rangle
+c_{3}\left\vert 001\right\rangle $. The coefficients ($ c_{0}$, $c_{1}$,
$c_{2}$, and $c_{3}$) can be manipulated through interaction parameters
($\left\vert \alpha \right\vert $, $\phi $, and $T$). In line with Xie and
Eberly's work[Phys. Rev. Lett. 127, 040403 (2021)], we investigate the genuine
tripartite entanglement for $\left\vert \psi \right\rangle _{123}$ using the
concurrence triangle measure. Drawing on Hao et al.'s research [Phys. Rev.
Lett. 128, 120402 (2021)], we examine tripartite steering for $\left\vert \psi
\right\rangle _{123}$ under certain measurements based on the uncertainty
relations criterion. We identify nine potential configurations exhibiting
varying steerability across different parameter spaces. It is important to
highlight that while the state $% \left\vert \psi \right\rangle _{123}$
exhibits entanglement, steering remains unattainable in a substantial portion
of the parameter space.
