What is a cognate enhancer sequence?
Cognate means of common origin.

In molecular biology, cognate is used to refer to known interacting pairs of functional entities. For example, cognate receptor of a ligand means the primary (default) receptor with which this ligand interacts. Similarly, cognate sites (which also includes enhancer) of a transcription factor (TF) refers to the well known and validated binding sites of the TF.

Also see this post.