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The observational evidence regarding the present cosmological aspects tellsus about the presence of very little anisotropy in the universe on a largescale. Here, in this paper, we attempt to study locally rotationally symmetric(LRS) homogeneous Bianchi-I spacetime with the isotropic matter distribution.This is done within the framework of $f(\mathcal{R},\mathscr{L}_m)$ gravity.Particularly, we consider a non-linear $f(\mathcal{R},\mathscr{L}_m)$ model,$f(\mathcal{R},\mathscr{L}_m)=\dfrac{1}{2}\mathcal{R}+\mathscr{L}_m^{\,{\alpha}}$.Furthermore, $\omega$, the equation of state parameter, which is vital stuff indetermining the present phase of the universe is constrained. To constrain themodel parameters and the equation of state parameter, we use 57 Hubble datapoints and 1048 Pantheon supernovae type Ia data sample. And, for ourstatistical analysis, we use Markoc Chain Monte Carlo (MCMC) simulation.Moreover, with the help of obtained values of parameters, we measure theanisotropy parameter for our model.

Constraining Anisotropic Cosmological Model in $f(\mathcal{R},\mathscr{L}_m)$ Gravity