In other words, junior brings home a new girlfriend, but the Dad gets to hit it before Junior gets to marry her. Are there any cultures that do that, if so, which ones do this?
No.
But people are always coming up with bizarre sexual customs for other people’s cultures, or their own culture in the past. For as close as you’re likely to get, check out this article, especially the last sentence: Wikipedia on Droit de Seigneur.
Maybe you can start a new trend.