  This study explores the cosmological implications of a modified $f(Q, B)$
gravity model, incorporating both the nonmetricity scalar ($Q$) and the
boundary term ($B$). A generic connection ($\Gamma_{\mu \nu}^{\alpha}$) has
been used to define the four-dimensional metric tensor and the covariant
derivative ($\nabla_{\mu}$). Statistical analysis using Markov Chain Monte
Carlo (MCMC) techniques constrains the $H(z)$ model free parameters based on
observational data from the Cosmic Chronometers (CC) sample, the extended
Pantheon$^+$ dataset, and Baryonic Acoustic Oscillation (BAO) measurements.
This analysis clarifies the deceleration and Equation of State (EoS) parameters
and reveals a smooth transition from a deceleration to an accelerating
expansion phase in the evolution history of the Universe. The most intriguing
finding is identifying a stable critical point within the dynamical system of
the model. This critical point corresponds to the de Sitter phase, a well-known
era of accelerated expansion. The stability of the critical point suggests
that, under specific initial conditions, the trajectory of the Universe will
inherently be drawn towards and remain within the de Sitter phase. This aligns
with the current observations, indicating that the Universe is dominated by
dark energy (DE) and undergoing late-time accelerated expansion.
