Cota made his professional debut for Pachuca on 21 September 2007 against Veracruz.[2]
Puebla
In 2014 it was announced Cota was sent out on loan to Puebla.[5] He made his debut against Tijuana in a 1–0 victory.[6] In April 2015, he won the Copa MX after defeating Guadalajara.[7]
Guadalajara
On 11 June 2015, Guadalajara announced they had signed Cota on loan in order to create competition with José Antonio Rodríguez, after club veteran Luis Ernesto Michel was sold to Dorados de Sinaloa. Cota then quickly rose to be the first-choice goalkeeper after his performances in the Copa MX, becoming champion after defeating Monarcas Morelia the Copa MX final, and became a key figure in the club's twelfth Liga MX title win against Tigres UANL.[8][9] He was named in the Best XI of the tournament and won the Golden Glove award for the season.[10][11]
On 16 May 2018, Cota was loaned out to Pachuca's sibling club León.[15]
Cota controversially wore a jersey to protest against femicide in Mexico during a match against Club Necaxa on 22 February 2020. The shirt had the figure of a woman lying in a pool of blood in the shape of a map of Mexico. Cota may be suspended for three matches and fined MXN $300,000 (US$15,000).[16]
Cota was included in the preliminary roster for the 2017 FIFA Confederations Cup in Russia as a replacement for José de Jesús Corona since he picked up an injury.[20] Cota made his debut on 1 June 2017 in a friendly match against Ireland at MetLife Stadium in New Jersey, concluding in a 3–1 victory.[21] Cota was subsequently included in Mexico's final roster for the tournament.[22]
In October 2022, Cota was named in Mexico's preliminary 31-man squad for the 2022 FIFA World Cup, and in November, he was ultimately included in the final 26-man roster, but did not receive any minutes on the field during the tournament.[23]