The short version from Wikipedia is this:
The Yemenite Children Affair (Hebrew: פרשת ילדי תימן) was the disappearance of hundreds of babies and toddlers of new immigrants to the newly founded state of Israel, mainly from Yemen, between the years 1948 to 1954. Most cases involved the parents being told in the hospital that their newborn children had died although they never received additional reliable information about their fates. The parents claim that their children were really kidnapped and given or sold to Ashkenazi families. In several cases, the children tracked down their parents many years later and conclusively determined their relationship to their Yemenite relations using DNA testing.
It’s in the news at the moment.
Here is a great page compiling many links on the topic.