Is it advisable to use iron supplementation in treating akathisia?

Possibly: There are case reports of patients with akathisia and low serum iron improving with IV iron supplementation, but it is not clear that it works in all cases or that it truly even worked in those patients. A randomized control (or even case-control) study would clarify the issue more. It is worth exploring, and the side effects are likely to be low (if pills, constipation, if iv, having an iv).

No: Some people with restless leg syndrome are iron deficient, but I am unaware of any connection with akasthesia, which usually is a result of a drug side effect. Withdrawing or lessening the dose of the offending drug is the primary treatment, and use of beta blockers and anticholinergic drugs like Cogentin (benztropine) etc. Are the next best things. Benzos like Clonazepam may help but produce dependency.