Constraining the dark energy deceleration parameter is one of the fascinating topics in the recent cosmological paradigm. This work aims to reconstruct the dark energy using parametrization of the deceleration parameter in a flat FRW universe filled with radiation, dark energy, and pressure-less dark matter. Thus, we have considered four well-motivated parameterizations of q(z), which can provide the evolution scenario from the deceleration to acceleration phase of the Universe. We have evaluated the expression of the corresponding Hubble parameter of each parametrization by imposing it into the Friedmann equation. We have constrained the model parameter through H(z), Pantheon, and baryons acoustic oscillation (BOA) data. Next, we have estimated the best-fit values of the model parameters by using Monte Carlo Markov Chain (MCMC) technique and implementing H(z)+ BAO+SNe-Ia dataset. Then we analyzed the cosmographic parameter, such as deceleration, jerk, and snap parameters, graphically by employing the best-fit values of the model parameter. Moreover, we have analyzed statefinder and Om diagnostics parameters for each scenario to discriminate various dark energy models. Using the information criteria, the viability of the models have examined. In the end, we have analogized our outcomes with the standard {\Lambda}CDM model to examine the viability of our models

This study examines accelerated cosmic expansion using the Viscous Modified Chaplygin Gas (VMMG) and Generalized Cosmic Chaplygin Gas (GCCM) within Horava-Lifshitz gravity. Our aim is to constrain essential cosmological parameters, such as the Hubble Parameter ($H_{0}$) and Sound Horizon ($r_{d}$). We utilize late-time datasets: 17 Baryon Acoustic Oscillation observations, 33 Cosmic Chronometer measurements, 40 Type Ia Supernovae data points, 24 quasar Hubble diagram data points, and 162 Gamma Ray Bursts data points, along with the latest determination of the Hubble constant (R22). Treating $r_{d}$ as a free parameter offers several advantages, including mitigating bias, enhancing precision, and improving compatibility with various datasets. By introducing random correlations in the covariance matrix during simulation, errors are effectively reduced. Our estimated values of the Hubble constant ($H_0$) and $r_{d}$ consistently align with measurements from both the Planck and SDSS experiments. Cosmographic tests provide valuable insights into the dynamics of various cosmological models, enriching our understanding of cosmic evolution. Statefinder diagnostics offer deeper insights into cosmic expansion dynamics, aiding in distinguishing between cosmological frameworks. Furthermore, the $o_{m}$ diagnostic test reveals that at late times, VMMG falls into the phantom region, while GCCM falls into the quintessence region. The Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) support all models, indicating plausible explanations. Notably, the $\Lambda$CDM model emerges with the lowest AIC score, suggesting its relatively superior fit. Validation via the reduced $\chi_{\text{red}}^{2}$ statistic confirms satisfactory fits across all models, reinforcing their credibility.