The eldest of the three, Selina, won silver, resulting in an outburst of emotions in the Gasparin family.
"I am so proud of my sister's achievements; she is the reason why Elisa and I followed in her footsteps. When we look at this moment 20 years down the line, we will remember with the fondest of memories," Aita said.
Selina dedicated her hardware to her sisters and her family.
"It is amazing to share this with them."
Biathlon is a family affair for the Gasparin sisters, who made history at the World Cup in 2012 in Austria by becoming the first three siblings to take part in a relay competition together.
Aita, who also participated in the Winter Youth Olympic Games in Innsbruck in 2012, said that the Sochi Games were all the more memorable for her because of all the moments spent with her sisters during training and in the Olympic Village.
"I wasn't always this close to my sisters. My elder sister Selina left to pursue biathlon in Norway when I was six. But now we all travel together, train together. We are together every day, 24/7."
The sisters congratulated each other with a hug while cameras flashed to the delight of the proud parents at the Laura biathlon centre as the crowd cheered them on.
Silver medallist Selina backs her youngest sibling, saying that she has a bright future ahead.
"My sisters, they now have better conditions than I had when I started," she said. "This together means they will be better than me."
The Gasparins have helped develop the sport for Swiss women. They have built two shooting targets near their childhood home and also established three more ranges around Switzerland.
Elisa finished in 33rd place, while Aita claimed the 62nd spot in the final rankings.