In what compounds does oxygen exhibit +½ oxidation state?
Yes. The dioxygenyl ion, $\ce{O_{2}^+}$, is a rarely-encountered oxycation in which both oxygen atoms have a formal oxidation state of +1/2. It is formally derived from oxygen by the removal of an electron:

$$\ce{O_{2} → O_{2}^+ + e^{-}}$$

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