Probing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ϕ</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:math> interaction through bound states of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ϕ

The possible bound state of the $\ensuremath{\phi}N\text{\ensuremath{-}}\ensuremath{\alpha}$ system is explored within the framework of the three-body cluster model. The calculations are done by employing the state-of-the-art $\ensuremath{\phi}N$ interactions obtained from the analysis of the pure elastic scattering and the coupled-channel in the $\ensuremath{\phi}p$ correlation functions. The $\ensuremath{\phi}\ensuremath{\alpha}$ potentials are constructed by two methods: the single-folding potential (SFP) method for the given spin-averaged $\ensuremath{\phi}N$ potentials in coordinate space, and the optical-model potential (OMP) approximation within the multiple-scattering framework for the given scattering length of the $\ensuremath{\phi}N$ interaction. It is found that, when only the single-channel $\ensuremath{\phi}N$ interactions are employed, the $\ensuremath{\phi}N\text{\ensuremath{-}}\ensuremath{\alpha}$ system could be bound with a binding energy in the interval [3--26] MeV. However, the coupled-channel $\ensuremath{\phi}p$ interaction, which is most consistent with experimental measurements, does not yield any bound state, even when the spin-averaged $\ensuremath{\phi}N$ potential is employed, and this potential is found to be more attractive than the corresponding coupled-channel counterpart. It is essential to consider the contributions from the dynamics of the vector-baryon coupled channels $\ensuremath{\phi}p$ interaction. This effect is capable of playing a decisive role in the existence of mesic nuclei.