  Dark energy can be characterized by a canonical scalar field, known as
quintessence. Quintessence allows for a dynamical equation of state $-1 \le
\omega \le -\frac{1}{3}$. In this work, we consider a quintessence model with a
specific potential of the Woods-Saxon form. The model is studied at late phase
assuming flat cosmology, and the model parameters are constrained using Type Ia
supernova data and Observational Hubble data. In particular we employ Markov
Chain Monte Carlo methods for the Bayesian inference of these parameters. We
obtain the value of the Hubble constant $H_0 = 68.10 \pm 0.74\,km s^{-1}
Mpc^{-1}$ and the matter energy density parameter $\Omega_{m_0} = 0.31 \pm 0.01
$, which are consistent with the values obtained using base $\Lambda$CDM using
the same dataset. Computation of the $\chi^2_{min}$, AIC and BIC reveal that
this model is preffered according to AIC and $\chi^2_{min}$ criteria, while the
$\Lambda$CDM is preferred according to BIC. We also show that this model can
explain late-time accelerated expansion. Statefinder analysis reveals a
Chaplygin gas behaviour in the past, in addition to the quintessence behaviour
of the field.
