Born in A Coruña, Galicia, Mosquera played roller hockey for his high school team in neighbouring Santa María del Mar.[1] In 2000, at the age of 12, he arrived in Real Madrid's youth system. He started out as a professional in 2006–07's Segunda División – four games, 84 minutes and relegation.[2]
On 24 January 2010, Mosquera was called to the first team for a match against Málaga, but did not leave the bench.[3] Two months and one day later he made his La Liga debut, playing one minute in a 4–2 away win over Getafe after replacing Xabi Alonso.[4]
Mosquera signed precisely with Getafe on 12 July 2010, penning a five-year contract and reuniting with former Real Madrid Castilla coach Míchel.[5] He made his debut for the club 16 days later, scoring against Germany's VfL Osnabrück in a friendly.[6]
On 20 January 2012, after not playing one single minute under new manager Luis García in the season, Mosquera agreed to return to Castilla, with the side in the Segunda División B.[7] In summer 2014, after a further top-flight campaign with Getafe, he joined Elche of the same league on a three-year contract.[8] He scored his first goal in the Spanish top tier on 14 September while at the service of the latter, contributing to a 3–2 away victory over Rayo Vallecano.[9]
Mosquera cut ties with the Valencians on 27 July 2015,[10] and signed a four-year deal with Deportivo de La Coruña hours later.[11] He played 37 matches in his first season, helping to a final 15th position in the table.[12]
On 2 August 2019, Mosquera terminated his contract at the Estadio Riazor[13] and joined Huesca for two years the following day.[14] During his spell in Aragon, he totalled 100 appearances.[15]
^De La Cruz, Luis (12 November 2018). "Mosquera, centenario agridulce" [Mosquera, bittersweet century] (in Spanish). Diario AS. Retrieved 14 August 2019.