  In this paper, we investigate the kinetically coupled early dark energy (EDE)
and scalar field dark matter to address cosmological tensions. The EDE model
presents an intriguing theoretical approach to resolving the Hubble tension,
but it exacerbates the large-scale structure tension. We consider the
interaction between dark matter and EDE, such that the drag of dark energy on
dark matter suppresses structure growth, which can alleviate large-scale
structure tension. We replace cold dark matter with scalar field dark matter,
which has the property of suppressing structure growth on small scales. We
employed the Markov Chain Monte Carlo method to constrain the model parameters,
our new model reveals a non-zero coupling constant of $0.030 \pm 0.026$ at a
68% confidence level. The coupled model yields the Hubble constant value of
$72.38^{+0.71}_{-0.82}$ km/s/Mpc, which resolves the Hubble tension. However,
similar to the EDE model, it also obtains a larger $S_8$ value compared to the
$\Lambda$CDM model, further exacerbating the large-scale structure tension. The
EDE model and the new model yield the best-fit values of $0.8316$ and $0.8146$
for $S_8$, respectively, indicating that the new model partially alleviates the
negative effect of the EDE model. However, this signature disappears when
comparing marginalised posterior probabilities, and both models produce similar
results. The values obtained from the EDE model and the new model are
$0.822^{+0.011}_{-0.0093}$ and $0.819^{+0.013}_{-0.0092}$, respectively, at a
68% confidence level.
