This work presents accurate {\it ab initio} investigations of various spectroscopic properties of a few Li-like ions in presence of a plasma environment within the Debye screening potential. The coupled-cluster theory in the relativistic framework has been employed to compute ionization potentials, excitation energies, electric dipole oscillator strengths, and electric quadrupole transition probabilities of Li-like C$^{3+}$, N$^{4+}$, and O$^{5+}$ ions. The unretarded Breit interaction has been implemented to increase the accuracy of the calculations. The effects of ion density and temperature on the ionization potentials, excitation energies, electric dipole oscillator strengths, and electric quadrupole transition probabilities have been investigated in the plasma environment. It is found that the plasma screening leads to a sharp decrease in the ionization potential as the screening strength increases. With increasing strength, the oscillator strengths associated with 2$s ^{2}S_{1/2}$$\rightarrow2 p ^{2}P_{1/2, 3/2}$ transitions increase, whereas the transition probabilities associated with 3$d ^2D_{3/2, 5/2}$$\rightarrow2 s ^2S_{1/2}$ transitions decrease.
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