Duke of Every Sin by Stacy Reid

Ethan Benedict, Duke of Bainbridge, has been an object of fascination and salacious gossip for years. His reputation would make him an unlikely savior of a baby left on his doorstep; however, Ethan saw the child as perhaps a pathway to redemption. He did not anticipate his jaded heart to soften toward the mysterious young lady who infiltrates his household claiming the child belongs with her.
Soon a marriage of convenience bargain is struck with little in the way of inconveniencing the duke until he starts to fall for his new bride. As their romance grows, so does the undeniable risk that everything might fall apart if his duchess discovers the full sins of his past.

*Duke of Every Sin was previously published in the Big Duke Energy anthology.