We investigate the dynamics of an algebraically coupled quintessence field with a dark matter fluid, focusing on particle production through the action principle via a modified interaction Lagrangian. The interaction parameter serves as the source of dark matter particle production and entropy generation. As particle creation occurs due to the interaction between the field and fluid sectors, the system exhibits additional pressure. Our analysis includes studying the system's dynamics by considering an exponential type of interaction corresponding to the field's exponential potential. We assess the system's background dynamics using the dynamical system stability technique to derive the constraints on the model parameters. Additionally, we determine the best-fit values of the model parameters against two combinations of data sets: (i) CC+Pantheon+SH0ES, and (ii) CC+Pantheon+SH0ES+SDSS BAO+ DESI BAO. By employing a comprehensive data analysis technique, we compare the evidence of our models to flat $Λ$CDM. Based on the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), one of the models emerges as a robust alternative to $Λ$CDM when considering the joint data sets.

32 pages, 16 figures, and 5 tables. Accepted for the publication in Chinese Journal of Physics