If the surname you are working with randomly interchanges -io- and -e- (e.g. Basenok/Basionok, Shlemov/Shliomov), it is likely that the original was -yo- (Cyrillic “ё”). -io- is an old way of writing “yo” sound, before letter “ё” became the norm. -e-, of course, just a common way of writing “ё”, not bothering with the trema.
Basenok/Basionok – Басенок, Басионок = Басёнок
Shlemov/Shliomov – Шлемов, Шлиомов = Шлёмов
http://en.wikipedia.org/wiki/Yo_(Cyrillic)
http://en.wikipedia.org/wiki/Diaeresis_(diacritic)#Vowels
Смотрите также: “Днепропетровский архив: метрические книги сел Верхнеднепровского уезда за 1917-1923 гг” и “Фамилии жителей с. Ольгинское за 1889 год”.