Hi again Michele,

I found this article about Rykun, it has a lot of information, and it includes this person's name:
Gesiya Mednikova.  Maybe someone from your  Mednikov family?

History of Jewish Communities in Ukraine
http://jewua.org/rykun/

Good luck in your search,

Sherri Bobish

Searching:
RATOWSKY / CHAIMSON (Ariogala / Rogala, Lith.)
WALTZMAN / WALZMAN (Ustrzyki Dolne / Istryker, Pol.)
LEVY / BRANDT (Tyrawa Woloska, Pol.)
BOJDA / BLEIWEISS (Tarnow & Tarnobrzeg, Pol.)
LEFFENFELD / ROSENWASSER / KALTER (Daliowa & Jasliska, Pol.)
SOLON / SOLAN / SOKOLSKY (Grodek, Bialystok, Pol.)
BOBISH / APPEL (Odessa ?)