(1) 北方方言。差：歪，斜 vernacular usage in certain parts of north china 差：歪，斜，sloping, askew. 这个女孩子戴差帽子. The girl has her hat askew. (2) 北方方言。 差：错 vernacular usage in certain parts of north china. 差：错, faulse, mistakenly. 这个女孩戴差帽子 The girl mistakenly tooked other's hat./ The girl took other's hat by err. The second is more probable.

It's added to a verb or adjective to indicate a continued action or state.

表示状态就是戴着，，如果是表示动作就可以直接说戴帽子。。不知道你能明白吗？

meaning, like, an "ing". Not "putting on", but just, like, "she's wearing a hat".