Despite the fact that the mass of the neutrinos is so small, they are produced in such vast numbers in the early Universe that their mass induces subtle effects on cosmological observables, primarily the growth of structure and the expansion history in the Universe. We consider the models where neutrino interacts with dark energy scalar field models; phantom, quintessence, and quintom. Also, we obtained the $$z_\textrm{nr}$$ $z_{\text{nr}}$ (the redshift at which a mass of neutrino $$m_{\nu }$$ $m_{\nu }$ will become non-relativistic) and surveyed the effect of non-relativistic neutrinos on the structure formation. The data used in this paper are Pantheon + Analysis catalog, CMB, and BAO data. We obtained coupling constant $$\beta $$ $\beta$ for neutrino and three scalar fields and found that larger $$\beta $$ $\beta$ values will generally lead to larger neutrino mass in the Universe. For combination data, we found that the total mass of neutrino $$\sum m_{\nu }< 0.1197$$ $\sum m_{\nu }<0.1197$ eV $$(95\% $$ $(95\%$ confidence level (C.L.) for quintom model and $$\sum m_{\nu }< 0.121 $$ $\sum m_{\nu }<0.121$ eV $$(95\% $$ $(95\%$ confidence level (C.L.) for phantom model and $$\sum m_{\nu }< 0.122$$ $\sum m_{\nu }<0.122$ eV $$(95\% $$ $(95\%$ confidence level (C.L.) for quintessence model. These results are in broad agreement with the results of Planck 2018 where the total neutrino mass is $$\sum m_{\nu }<0.12$$ $\sum m_{\nu }<0.12$ eV ( $$95\%$$ $95\%$ C.L., TT, TE, EE + lowE + lensing + BAO). Using the neutrino mass obtained from different models, we calculated $$z_\textrm{nr}$$ $z_{\text{nr}}$ and co-moving wave number $$k_\textrm{nr}$$ $k_{\text{nr}}$ and showed that neutrinos played a role on the structure formation in the early Universe.