Fasciation is caused by a lot of things, some genetic and some physical (disease, bug bite, chemical reaction...). It happens when the apical meristem (the growth point), for some reason becomes elongated, rather than staying a point. The only way the fasciation might be repeated in the next generation if the cause was genetic. Here's a good short article explaining it a little better than I.
https://mdc.mo.gov/blogs/fresh...