One summer day, a baby appears on the literal doorstep of the Imperial Residence's west servants' entrance. She is in a basket. She doesn't look Barrayaran; while Barrayar is not uniformly Caucasian, it has very few people of east Asian extraction, and that is where this baby appears to have been toted from by more or less circuitous routes of migration and inheritance.
It is not terribly difficult for ImpSec to find the person who put her there - recent hire to the kitchen staff, competent but not overwhelmingly concerned with security when it was literally just a baby and not an explosive and he was offered a large chunk of change. Tracing back this chunk of change leads through a long meandering trail of people, variously shady, none of whom acted with particular malice beyond greed and the sort of vague dishonorableness of putting packages on the doorstep of the Imperial Residence.
The trail ends at someone who - under fast-penta - has no memory whatever of having interacted with the baby, the cash, the shady person who druggedly identified her, or anything else about the affair. She doesn't even have a similar-looking sister to explain the mixup. She has nothing in her background to explain how she would come by an offplanet baby or why she would convey it by such a circuitous method to the Imperial Residence. It's definitely not her baby - the lady's six months pregnant and the baby isn't that old.
In the meantime, the baby is parked with Droushnakovi, who found her in the first place; Cordelia, who was the first person she went to; and Gregor, as Drou is his personal bodyguard.
The baby and her basket are searched and found to be: a baby, and a basket. There is no note, it's the middle of summer and the child wasn't even in a blanket, the basket itself and the baby's onesie turn out to be local products that a Vorbarr Sultana thrift shop didn't even bother reporting stolen.
The baby babbles in her sleep. She's very cute.