Question: Can I use this epistemic expression: “He ***won’t have gone*** there yesterday”? It may not be ungrammatical, I think. But I have two questions. First, is this ‘*won’t have p.p.*’ used casually or freely to say that something might have happened in the past? Second, If it were present perfect, adverbs which denote the past would not be used. Then Is it, *yesterday*, okay in the example above?

Answer: 
This has nothing whatsoever to do with the future.

*He won't have gone there yesterday* is a modalized version of *He went there yesterday*, with the past time meaning carried by the perfect auxiliary *have*. The modality expressed by *won't* is a slight epistemic weakening. It would typically be taken as indicating that the speaker does not know this for a fact, and is merely stating confident speculation.

This expression could be used when contrasting with another time that they did go or will go.
I may be the contrarian here but I see a completely possible reading involving the future. Your example may be some dialect which I don't know and I'd be curious to see more of the context, but my interpretation is as follows:

Imagine that your sister is taking her boyfriend out for his birthday and you suggest that she take him to the State Fair, which started a few days ago. She might reply:

> 
> He won't have gone there yesterday?
> 
> 
> 

She's asking whether, in the future situation, he will already have been to the fair. This is proper English.