  A connection between the neutrino and an exotic fermion is described in the
general neutrino model. In this model the neutrinos can convert into the new
fermion and thus the interaction leads to novel recoil spectrum in the neutrino
scattering experiments. We study the general neutrino interaction by evaluating
both the tree-level and loop-level contributions to the coherent elastic
neutrino-nucleus scattering. We illustrate the scattering by taking the
framework of a simplified neutrino model with a Dirac fermion $\chi$ and a
spin-0 mediator. For the CP phase in the quark sector being 0 and $\pi/2$, the
detection processes are dominated by the tree-level and loop-level
contribution, respectively. We investigate the constraints on the couplings
between the mediator and the new particle $\chi$ or the quarks by fitting to
the COHERENT data. The parameter space with $m_\chi$ larger than the maximal
energy of incoming neutrinos can be also constrained by including the
loop-level contribution.
