In this paper, we employed the q-Bessel Tricomi functions of zero-order to introduce bivariate extended q-Laguerre-based Appell polynomials. Then, the bivariate extended q-Laguerre-based Appell polynomials were established in the sense of quasi-monomiality. We examined some of their properties, such as q-multiplicative operator property, q-derivative operator property and two q-integro-differential equations. Additionally, we acquired q-differential equations and operational representations for the new polynomials. Moreover, we drew the zeros of the bivariate extended q-Laguerre-based Bernoulli and Euler polynomials, forming 2D and 3D structures, and provided a table including approximate zeros of the bivariate extended q-Laguerre-based Bernoulli and Euler polynomials
