A progeny is an offspring or child of a vampire known as a maker.
In "The Southern Vampire Mysteries", this new vampire's maker usually teaches his or her progeny about how to survive as a vampire, providing guidance on glamouring, how to feed on humans, locations to sleep during the day, etc. This is not an obligation or rule, although abandoning one's progeny tends to lead to ridicule from other vampires. Furthermore, the chance of a progeny living out their first year as a vampire without the assistance of their maker is around 33%, with two out of every three abandoned progeny not making it.
Progeny's feelings towards their maker vary depending on the circumstances of the turning and personal outlook. Jessica, Nora and Eric regard their makers as their parents, while Bill, Pam, Talbot and other other vampires were turned because their makers were in love with them; therefore, their feelings aren't in the least parental.
A progeny may turn a vampire and become a maker themselves while still under the influence of their own maker. The "grandparent" has no actual control over the "grandchild".