Jefferson was spotted playing for a local side in Aylesbury, and was signed for Thame United of the South Midlands League at the age of 21, and helped them to win promotion to the Isthmian League Division 3. During the summer of 2001 however, he was found guilty of dangerous driving whilst disqualified, and served a six month prison sentence. Following his release, he rejoined Thame United in December 2001. It wasn't long before he came to the attention of some League sides, and he signed for Oxford United in March 2003. During his spell with the U's, he went on one moth loans to Woking in August 2004, and Gravesend & Northfleet in August 2004 before leaving to join Forest Green Rovers the following month for a short spell. He rejoined Woking in December 2004 until the end of the season, then had a brief spell at Bristol Rovers the following season before periods at Hemel Hampstead, Lewes, Worthing and Stevenage Borough. Short periods at Eastleigh, Yeading, Havant & Waterlooville, Weymouth, Maidenhead United and Mansfield Town followed before joining Wrexham for the 2008/2009 season. He made his one and only International appearance for Dominica whilst with the Stags. He scored 15 goals in 38 games for Wrexham. In the summer of 2009, Jefferson joined Crawley Town, scoring 5 goals in 18 appearances, and he arrived at Nene Park on 12 November 2009 on loan from the Red Devils. The deal was initially until 24 January 2010, but on that date the loan was extended through to the end of the 2009/10 season.

Jefferson made his Diamonds debut in the 2-1 victory over Histon on 14 November 2009, and scored his debut goal in his next game, against Cambridge United. He played for the club until the end of the 2009 / 2010 season when his loan expired. He was released by Crawley Town and on 9 June 2010, he joined Conference North side Gainsborough Trinity. On 8 October 2010, he went on a three month loan with Darlington with a view to a permanent deal, but this fell through and he returned to Trinity in January, where he was released. After playing a single game for Weymouth, on 21 January 2011, he joined Conference side Hayes & Yeading on a deal until the end of the season, but was released by mutual consent on 10 March 2011, joining Conference South side Maidenhead United the following day for the remainder of the season. In July 2011, he joined Southern League Premier side Brackley Town. He was released by Brackley after some six months, and signed for Conference side Lincoln City on 31 January 2012 until the end of the season.