Dockerty, 27, initially joined the club in 2019 from Hemsworth Miners, before returning for a second spell in September 2022 after a brief stint at Alfreton Town.
During his time at the club, he made 119 appearances and scored 23 goals.
Also departing the Horsfall Community Stadium is defender Mwakona.
The Zimbabwean defender, who spent time at Morecambe, made one appearance for Avenue.
In a statement, the club said: "We’d like to put on record our thanks to both Brad and Reward for their time at the club, and wish them both the best in their future careers."
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