The Black and Whites manager has stepped down from the role following Saturday’s 4-1 defeat to Queen’s Park which left the club three points adrift at the bottom on League 2.
The former Wick Academy manager left the Highland League club to succeed Ross Jack in January but City have not won a league match since August 23.
City director Martyn Hunter said: “Barry shares the real disappointment of recent results with both the club officials and supporters alike. His contribution to the club both as manager and previously as assistant manager is appreciated by the board and we wish Barry and his family all the best for the future.”