During her early teens, Pátková played with the women's representative team of
HC Litvínov in the
Czech Women's Extraliga (Extraliga žen) until 2016. At that time, she secured a scholarship to and began attending
The Gunnery, a
private boarding school in
Washington, Connecticut, United States known for its strong athletics programs. While a member of The Gunnary girls’ ice hockey team, which competes in the USA Hockey High School Girls League, she also played with the Connecticut Polar Bears U19 of the USA Hockey Girls Tier I Under-19 (19U AAA) League. Fellow Czech ex-pat and future national team teammate
Noemi Neubauerová was also Pátková's teammate at The Gunnery, and with the Connecticut Polar Bears U19. In 2018, Pátková relocated to the Hockey Training Institute (HTI) in
Mulmur,
Ontario, Canada, to play with the HTI Stars, an independent women's under-20 ice hockey team. She joined
Natálie Mlýnková and
Kateřina Zechovská as one of three Czech players on an international roster that included players from nine different countries. At the end of the season, Pátková and Mlýnková both committed to the
University of Vermont as incoming
freshmen for the
2019–20 season. == International play ==