Fewster, 25, joined the Blues in March 2019 from Blyth Spartans, having also spent time with Middlesbrough academy.
He has played for England at under-16, under-17, under-18 and under-19 level, and had loan spells with Football League sides Preston North End, York City and Hartlepool United, before joining Spennymoor Town in 2017.
Joint manager Lee Bullock said: "It's great that we've been able to get Brad signed on for anther season.
"If he wants to play professionally, the best way for him to do that is to stay on the pitch and score a bag full of goals, and we would like nothing more than to help him reach his dream.
"We would like to thank Brad for committing to the club."
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