A Double Barrelled Detective Story

Sherlock Holmes finds himself in the American west. The story contains two arcs of revenges. In the primary arc, a woman was abused, humiliated and abandoned by her fiancé Jacob Fuller, while she bore his child. The child was born and named Archy Stillman and when he got older, the mother discovered that the child possessed an incredible ability of smell, like a bloodhound. The mother instructed her child, now sixteen, to seek out his biological father, destroy that man's peace and reputation, hence extract satisfaction for her.