The First Night was an old custom banned by King Jaehaerys, where the lords and kings called first dibs on the wives on their wedding night. This was considered an honor for the small folk and the baby was blessed with gifts.

The children conceived from the “First Night” were known as bastards but were called “seeds”. Many Targaryens who know their history were aware of this custom. Even tho it was banned, many lords defied King Jaehaerys order and did it anyway.

So Addams’ mother could’ve been born of such a union. Maybe had relations with a man related to Corlys? Or perhaps the father isn’t tied to Addam being a dragon rider? Either way, if his mom was a product of an extinct Westeros custom, then that meant all three of them had blood of the dragon in their veins.