The 27-year-old was nominated alongside Charlie Wyke, Anthony Scully, Will Keane, Carl Winchester and Lewis Fiorini.
The Morecambe striker received 21 per cent of the votes to win the award, coming a week after he won a second consecutive League One player of the month prize.
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Stockton scored five league goals in as many games for the Shrimps during September with doubles against AFC Wimbledon and Accrington Stanley, as well as another in the victory over Lincoln City.
That took him to 11 for the season in all competitions, nine of which have come in League One and see him as the division’s joint top scorer alongside Ipswich Town’s Macauley Bonne.
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