Ajeti started his youth football with FC Concordia Basel, but came through the ranks at FC Basel, playing in the U-16, U-18 and U-21 teams.
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During the beginning of the season 2013–14 on 5 October 2013 Ajeti scored his first League goal in the 2–1 away win against Lausanne-Sport.
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Ajeti made his first team league debut as a substitute on 28 August 2011 in the 2:1 home win against FC Thun.
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On 6 February 2013 Ajeti made his debut for the Swiss U-21 team in the El Madrigal stadium in Villarreal, Spain.