In recent times, there have been several observations suggesting deviations from lepton universality in semileptonic decays of [Formula: see text] mesons. These deviations have been noticed both in the neutral-current transitions ([Formula: see text]) and charged-current transitions ([Formula: see text]). Motivated by these intriguing findings, we investigate the semileptonic decays involving the quark-level transitions of [Formula: see text]. To explore the presence of new physics, we adopt a model-independent approach and analyze the processes [Formula: see text], [Formula: see text] and [Formula: see text], where [Formula: see text] represent the four lightest excited charm mesons. Considering a comprehensive effective Hamiltonian, we perform a global fit using various sets of new coefficients and incorporate measurements of [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], as well as the upper limit on the branching ratio of [Formula: see text]. Subsequently, we examine the impact of constrained new couplings on the branching ratios, forward–backward asymmetry parameters, lepton nonuniversality (LNU) ratios, as well as lepton and hadron polarization asymmetries in these decay modes.