I think you've got some kind of adapter on the end of every read, so the half that is sample maps, and the half that is adapter is all mismatched. I'd eyeball your reads, see if you can spot a common sequence on all of them.
Thanks for the reply. So I downloaded this data from NCBi to do some data mining and noticed that it is a RAD-seq dataset. I am not sure whether this pattern is caused by the method or something else is going on.
PS: I am not really familiar with RAD-seq method.