Optical isomerism is common in octahedral complexes involving didentate ligands. We analyze the options based on their symmetry:

1. [Co(en)₃]³⁺: This is a complex of the type $[M(AA)_3]$. As per NCERT, complexes of this type are chiral and form distinct enantiomers (dextro and laevo) .
2. [Co(en)₂Cl₂]⁺: This is of the type $[M(AA)_2a_2]$. It shows geometrical isomerism (cis and trans). The cis-isomer is chiral (optically active) because it lacks a plane of symmetry. The trans-isomer is optically inactive . Since at least one isomer is active, the ion exhibits optical isomerism.
3. [Co(en)Cl₂(NH₃)₂]⁺: This unsymmetrical complex containing a bidentate ligand can exist in isomeric forms that lack elements of symmetry, thus exhibiting optical isomerism.
4. [Co(NH₃)₃Cl₃]: This is of the type $[Ma_3b_3]$. It exists as facial (fac) and meridional (mer) isomers. Both the fac and mer isomers possess planes of symmetry (achiral) and are optically inactive. Therefore, this complex does not exhibit optical isomerism .