During season 7 of Game of Thrones, various references were made towards Daenerys and her having children. She didn’t always react in a positive manner to the thought, as she believed she was unable to bear children after her stillbirth. Instead of a child in a traditional sense, she referred to her dragons as her children. However, after the night shared between her and Jon Snow things may have changed.
Jon Snow, previously believed to be the bastard child of Eddard Stark, is revealed to really be the son of Rhaegar Targaryen. His birth name was Aegon Targaryen. This revelation makes him not only a member of House Targaryen but also the rightful heir to the Iron Throne.
This supersedes Daenerys’ claim to the Iron Throne which could be a source of drama during season 8 of Game of Thrones when it returns. Unfortunately, this also means Jon/Aegon also is having relations with his aunt (Daenerys). Matters from there could only be further complicated by the birth of a child from their union during the season 7 finale.
If a child were to be born, it would have a future as the next Targaryen and future ruler of Westeros. This child would be the first rightful heir since the War of the Usurper which ended the previous Targaryen dynasty. Combined with Daenerys’ dragons and Jon being set up to be a legend in the war against the Night King, Westeros may be unified in a way unseen in generations. Thanks to Daenerys’ connections to the Dothraki, after claiming the Iron Throne she could usher an era of prosperity and peace. However, should there be concern over the shared ancestry of Jon and Daenerys?
Technically yes, as inbreeding as various risks which is why it’s frown upon even in Game of Thrones. Even with this, House Targaryen is known for inbreeding in order to preserve certain characteristics among descendants. Among numerous characteristics is the infamous platinum-blonde hair along with an affinity with dragons.
A negative side effect is that members of House Targaryen are known to be more likely to develop mental illness, with erratic and sometimes violent behavior nick-named the ‘Targaryen Madness.’ This could mean the child and potential future ruler of Westeros becomes its greatest ruler in generations or cursed to become mad and maybe one of the most dangerous foes Westeros ever witness.