on exhibition 的意思是“在展出”（=being shown to the public）。

The photographs are on exhibition until the end of September. 这些摄影作品将一直展览到9月底。

A collection of paintings by David Hockney is on exhibition at the Museum of Art. 戴维·霍克尼的一批绘画作品正在美术馆展出。

在美国英语中，exhibit 可用于表示 exhibition 的意思。如朗文词典对 exhibit 的解释如下(注意其中的第三条解释)：

1. something, for example a painting, that is put in a public place so that people can go to see it: The exhibits date from the 17th century.

2. an object that is shown in court to prove whether someone is guilty or not: Exhibit A is the hammer found next to the victim.

3. AmE an exhibition: a big exhibit in Milan

所以有时确实可以见到 on exhibit 的用法，意思与 on exhibition 相同，属美国英语。如：

On exhibit are new products of industry and agriculture. 展出的是工农业的新产品。