The Ashkenazi are Khazarian is mostly false, invented by themselves to dodge Christ killer allegations. The Ashkenazim got rich trading on the silk road around the Khazar empire and a small number of Khazar elite converted to get in on the trade but didn't really intermix.
That girl was either a Mizrahi or a colonizer. Who knows, maybe you knocked her up and a generation from now your son will be murdering Palestinian children (if there are any left by then)