Shouldn't it rather be आएगी? The pronunciation differs from अयेगी. Aye vs ae
The pronunciation is actually considered to be the same. "Standardized" Hindi spelling uses the Y in this case, but when the same formation occurs in other languages similar to Hindi, or when spelled by Hindi writers who are not totally familiar with the so-called standard, they may use आएगी. There is no such distinction when Hindi is spelled in Arabic alphabet.