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Utilizing a tritter with variable parameter $T$ and induced byvacuum-one-photon superpositions $\left\vert 0\right\rangle +\alpha \left\vert1\right\rangle $ with $\alpha =\left\vert \alpha \right\vert e^{i\phi }$, wegenerate 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 andEberly's work[Phys. Rev. Lett. 127, 040403 (2021)], we investigate the genuinetripartite entanglement for $\left\vert \psi \right\rangle _{123}$ using theconcurrence 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 uncertaintyrelations criterion. We identify nine potential configurations exhibitingvarying steerability across different parameter spaces. It is important tohighlight that while the state $% \left\vert \psi \right\rangle _{123}$exhibits entanglement, steering remains unattainable in a substantial portionof the parameter space.

Tripartite entanglement and tripartite steering in three-qubit pure states induced by vacuum-one-photon superpositions