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Scott, 22, joined the club in the summer and made four appearances, the last being in the 1-0 win over Worksop Town at the end of August.
A club statement said: “The former Manchester United man leaves with the clubs best wishes and hopes he is able to return to the professional game one day.
“Kidsgrove Athletic FC will not be making any more comment about this issue at the time.”
Scott has previously been with Altrincham and Newcastle Town.
He made two appearances for Hamilton Academical in the Scottish Premiership in 2018.
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