yudaron

its very simple why.
like most Gedolei Yisroel there are thousands of desecndants of RAE who are not Frum and not even Jewish.
The Chassam Sofer was Zoche that almost all of his offspring are Frum Jews .

Yes!
all the offspring of the Chasam Sofer are automatically from RAE
since he had no children from his first and third wives.