  We investigate the effects of a Non-Standard Interaction (NSI) extension of
the standard model of particle physics on solar neutrino flavour oscillations.
This NSI model introduces a $U_{Z^\prime}(1)$ gauge symmetry through a
$Z^\prime$ boson that mixes with the photon, creating a neutral current between
active neutrinos and matter fields via a unique coupling to up and down quarks.
The interaction is defined by a single parameter, $\zeta_o$, which is related
to the $Z^\prime$ boson's mass $m_{Z^\prime}$ and coupling constant
$g_{Z^\prime}$. Notably, this model relaxes the bounds on Coherent Elastic
Neutrino-Nucleus Scattering experiments and fits the experimental values of the
anomalous magnetic dipole moment of the muon. In this study, we use solar
neutrino measurements and an up-to-date standard solar model to evaluate the
neutrino flavour oscillations and assess the constraints on $\zeta_o$. Our
study indicates that the NSI model aligns with the current solar neutrino data
when $\zeta_o$ is between $-0.7$ and $0.002$. These models have $\chi^2_{\nu}$
values equal to or better than the standard neutrino flavor oscillation model,
which stands at a $\chi^2_{\nu}$ of 3.12. The best NSI model comes with a
$\zeta_o$ value of -0.2 and a $\chi^2_{\nu}$ of 2.96. Including extra data from
the Darwin experiment in our analysis refines the range of $\zeta_o$ values
from $-0.7$ to $0.002$, down to $-0.5$ to $-0.002$. These results hint at the
possible existence of novel interactions, given that NSI models achieve a
comparable or superior fit to the solar neutrino data when contrasted with the
prevailing standard model of neutrino flavour oscillation.
