W.C United Wildcats Quezada first participated in his local club soccer team, W.C United Wildcats which stands for West Chicago United Wildcats.
Chicago Fire After playing a short time with his high school program, Quezada was invited to a tryout with
Chicago Fire youth academy in the
Major League Soccer. Spending years in the clubs youth academy and developing.
Deportivo Cuenca In 2014 Quezada transferred to
Deportivo Cuenca (youth academy) of the
Serie A at just 16 years of age which he mentioned as having an exceptional infrastructure for developing young players in their system. Alexis attracted interest from a number of clubs, and eventually
Deportivo Cuenca won the race for his signature in February 2014.
Toluca was close in 2013 but passport problems prevented him from playing in Mexico.
Club Venados On July 6, 2016, Quezada received his Mexican nationality and was joining Mexican side
Venados F.C. of
Ascenso MX. Not playing much of his time due to injuries on his ankle. He did help
Cantera Venados obtain their first championship title in their institution youth system.
Club Celaya Before the second half of 2017–18, Quezada joined
Celaya in the
Ascenso MX now called
Liga de Expansión MX.
Leixões S.C. In 2020, it was announced that Quezada signed with
Segunda Liga Portugal side
Leixões. Debuting against
Boavista on December 18, 2021, in
Estádio do Bessa. He was also part of
Leixões very talented side Liga Revelação under-23 squad who were one victory away of becoming champions before losing against
Estoril 2–0. The match was terminated after a massive brawl occurred between both sides with minutes remaining.
AD Fafe In 2021, he joined Portuguese club side
Fafe in
Liga 3 (Portugal) Xanthi F.C. Alexis was officially signed to historic Greek club side
Xanthi. On April 10, 2022, he debuted for Xanthi in a 0–0 draw with
Panserraikos in the Super League 2.
Gualaceo S.C. Alexis signed for
Ecuadorian Serie A team
Gualaceo S.C.on January 23, 2023. He never made an official debut for Gualaceo before leaving the club in July 2023.
Estrela Da Amadora On August 2, 2024, Quezada completed a transfer to Portuguese
Primeira Liga side
Estrela Amadora, signing a one-year contract.
Jarabacoa FC Liga Dominicana de Fútbol side
Jarabacoa FC announced the signing of Quezada on August 9, 2025. His arrival in the Dominican Republic was cheered as a breakthrough, both on and off the field, and he was credited with helping to grow the sport and the league in the country. ==International career==