We have studied the A-site substitution effect on the structural, thermal, and magnetic properties of the infinite layer iron oxide AFeO(2) (A = alkali-earth elements) with an FeO(4) square-planar coordination. Together with the previous study showing a total substitution by Ca, Ba substitution is found to be tolerable up to 30%, presenting almost the same substitutional range as that found in ACuO(2) under high pressure. Notably, Ba substitution shows little influence on the magnetic properties, in contrast to expectations from first principles calculations. The temperature at which oxidation to an AFeO(2.5) phase occurs and its transformation rate show a wide variation tunable solely by the out-of-plane distance.[on SciFinder (R)]