<p>Motivated by the discovery of several kaon-like states observed at BESIII and LHCb, this study explores S-wave and P-wave tetraquark states with quark contents <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( ss\bar{s}\bar{q} \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>s</mi> <mi>s</mi> <mover accent="true"> <mrow> <mi>s</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> <mover accent="true"> <mrow> <mi>q</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\( sq\bar{q}\bar{q} \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>s</mi> <mi>q</mi> <mover accent="true"> <mrow> <mi>q</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> <mover accent="true"> <mrow> <mi>q</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> </mrow> </math></EquationSource> </InlineEquation> using potential-based phenomenology. The tetraquarks are modeled as diquark-antidiquark systems in antitriplet-triplet and sextet-antisextet color configurations. The mass spectra are calculated using the Cornell potential, while decay properties are analyzed through Fierz rearrangement. A comparison with experimentally observed states is provided to enhance our understanding of light-light tetraquark systems with non-homogeneous quark compositions.</p>