Your queen will try not mate with any of the drones from your yard. Your drones usually only fly about a kilometer from their hives. The queen will probably triple that so that she does not mate with her own bees.
If she does mate with her sons, half of the bees will bee an exact copy of the queen and the bees will remove them. The other half will be half her fathers genes and will bee allowed to developer. If it does happen, when she is laying eggs from her sons, the brood pattern will be very spotty with only half of them developing. The bees will usually supersede her.